Hands On Exercise 11 Processing and Visualisng Flow Data

1.0 Overview

Spatial interaction represent the flow of people, material, or information between locations in geographical space. It encompasses everything from freight shipments, energy flows, and the global trade in rare antiquities, to flight schedules, rush hour woes, and pedestrian foot traffic.

Each spatial interaction, as an analogy for a set of movements, is composed of a discrete origin/destination pair. Each pair can be represented as a cell in a matrix where rows are related to the locations (centroids) of origin, while columns are related to locations (centroids) of destination. Such a matrix is commonly known as an origin/destination matrix, or a spatial interaction matrix.

In this hands-on exercise, you will learn how to build an OD matrix by using Passenger Volume by Origin Destination Bus Stops data set downloaded from LTA DataMall. By the end of this hands-on exercise, you will be able:

• to import and extract OD data for a selected time interval,

• to import and save geospatial data (i.e. bus stops and mpsz) into sf tibble data frame objects,

• to populate planning subzone code into bus stops sf tibble data frame,

• to construct desire lines geospatial data from the OD data, and

• to visualise passenger volume by origin and destination bus stops by using the desire lines data.

2.0 Getting Started

For the purpose of this exercise, seven r packages will be used. They are:

• sf for importing, integrating, processing and transforming geospatial data.

• tidyverse for importing, integrating, wrangling and visualising data.

• tmap for creating elegent and cartographic quality thematic maps.

• stplanr provides functions for solving common problems in transport planning and modelling such as downloading and cleaning transport datasets; creating geographic “desire lines” from origin-destination (OD) data; route assignment, locally and interfaces to routing services such as CycleStreets.net; calculation of route segment attributes such as bearing and aggregate flow; and ‘travel watershed’ analysis.

• DT provides an R interface to the JavaScript library DataTables. R data objects (matrices or data frames) can be displayed as tables on HTML pages, and DataTables provides filtering, pagination, sorting, and many other features in the tables.

Code

pacman::p_load(tmap, sf, DT, stplanr, tidyverse, sp, performance, reshape2, ggpubr)

3.0 Preparing the Flow Data

3.1 Importing the OD data

Firstly, we will import the Passenger Volume by Origin Destination Bus Stops data set downloaded from LTA DataMall by using read_csv() of readr package.

Code

odbus <- read_csv("data/aspatial/origin_destination_bus_202210.csv")

Let use display the odbus tibble data table by using the code chunk below.

Code

glimpse(odbus)

Rows: 5,122,925
Columns: 7
$ YEAR_MONTH          <chr> "2022-10", "2022-10", "2022-10", "2022-10", "2022-…
$ DAY_TYPE            <chr> "WEEKDAY", "WEEKENDS/HOLIDAY", "WEEKENDS/HOLIDAY",…
$ TIME_PER_HOUR       <dbl> 10, 10, 7, 11, 16, 16, 20, 7, 7, 11, 11, 8, 11, 11…
$ PT_TYPE             <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE      <dbl> 65239, 65239, 23519, 52509, 54349, 54349, 43371, 8…
$ DESTINATION_PT_CODE <dbl> 65159, 65159, 23311, 42041, 53241, 53241, 14139, 9…
$ TOTAL_TRIPS         <dbl> 2, 1, 2, 1, 1, 4, 1, 3, 1, 5, 2, 5, 15, 40, 1, 1, …

A quick check of odbus tibble data frame shows that the values in OROGIN_PT_CODE and DESTINATON_PT_CODE are in numeric data type. Hence, the code chunk below is used to convert these data values into character data type.

Code

odbus$ORIGIN_PT_CODE <- as.factor(odbus$ORIGIN_PT_CODE)
odbus$DESTINATION_PT_CODE <- as.factor(odbus$DESTINATION_PT_CODE) 

3.2 Extracting the study data

For the purpose of this exercise, we will extract commuting flows on weekday and between 6 and 9 o’clock.

Code

odbus6_9 <- odbus %>%
  filter(DAY_TYPE == "WEEKDAY") %>%
  filter(TIME_PER_HOUR >= 6 &
           TIME_PER_HOUR <= 9) %>%
  group_by(ORIGIN_PT_CODE,
           DESTINATION_PT_CODE) %>%
  summarise(TRIPS = sum(TOTAL_TRIPS))

Table below shows the content of odbus6_9

Code

datatable(odbus6_9)

We will save the output in rds format for future used.

Code

write_rds(odbus6_9, "data/rds/odbus6_9.rds")

The code chunk below will be used to import the save odbus6_9.rds into R environment.

Code

odbus6_9 <- read_rds("data/rds/odbus6_9.rds")

4.0 Working with Geospatial Data

For the purpose of this exercise, two geospatial data will be used. They are:

BusStop: This data provides the location of bus stop as at last quarter of 2022. MPSZ-2019: This data provides the sub-zone boundary of URA Master Plan 2019.

Both data sets are in ESRI shapefile format.

4.1 Importing geo-spatial data

Two geospatial data will be used in this exercise, they are:

Code

busstop <- st_read(dsn = "data/geospatial",
                   layer = "BusStop") %>%
  st_transform(crs = 3414)

Reading layer `BusStop' from data source 
  `C:\j00b00\IS415-GAA\Hands-on_EX\Hands-on_Ex11\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 5159 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21

Code

mpsz <- st_read(dsn = "data/geospatial",
                   layer = "MPSZ-2019") %>%
  st_transform(crs = 3414)

Reading layer `MPSZ-2019' from data source 
  `C:\j00b00\IS415-GAA\Hands-on_EX\Hands-on_Ex11\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS:  WGS 84

Code

mpsz

Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM
First 10 features:
                 SUBZONE_N SUBZONE_C       PLN_AREA_N PLN_AREA_C       REGION_N
1              MARINA EAST    MESZ01      MARINA EAST         ME CENTRAL REGION
2         INSTITUTION HILL    RVSZ05     RIVER VALLEY         RV CENTRAL REGION
3           ROBERTSON QUAY    SRSZ01  SINGAPORE RIVER         SR CENTRAL REGION
4  JURONG ISLAND AND BUKOM    WISZ01  WESTERN ISLANDS         WI    WEST REGION
5             FORT CANNING    MUSZ02           MUSEUM         MU CENTRAL REGION
6         MARINA EAST (MP)    MPSZ05    MARINE PARADE         MP CENTRAL REGION
7                   SUDONG    WISZ03  WESTERN ISLANDS         WI    WEST REGION
8                  SEMAKAU    WISZ02  WESTERN ISLANDS         WI    WEST REGION
9           SOUTHERN GROUP    SISZ02 SOUTHERN ISLANDS         SI CENTRAL REGION
10                 SENTOSA    SISZ01 SOUTHERN ISLANDS         SI CENTRAL REGION
   REGION_C                       geometry
1        CR MULTIPOLYGON (((33222.98 29...
2        CR MULTIPOLYGON (((28481.45 30...
3        CR MULTIPOLYGON (((28087.34 30...
4        WR MULTIPOLYGON (((14557.7 304...
5        CR MULTIPOLYGON (((29542.53 31...
6        CR MULTIPOLYGON (((35279.55 30...
7        WR MULTIPOLYGON (((15772.59 21...
8        WR MULTIPOLYGON (((19843.41 21...
9        CR MULTIPOLYGON (((30870.53 22...
10       CR MULTIPOLYGON (((26879.04 26...

The code chunk below will be used to write mpsz sf tibble data frame into an rds file for future use.

Code

mpsz <- write_rds(mpsz, "data/rds/mpsz.rds")

5.0 Geospatial data wrangling

5.1 Combining Busstop and mpsz

Code chunk below populates the planning subzone code (i.e. SUBZONE_C) of mpsz sf data frame into busstop sf data frame.

Code

busstop_mpsz <- st_intersection(busstop, mpsz) %>%
  select(BUS_STOP_N, SUBZONE_C) %>%
  st_drop_geometry()

Code

datatable(busstop_mpsz)

Before moving to the next step, it is wise to save the output into rds format.

Code

write_rds(busstop_mpsz, "data/rds/busstop_mpsz.rds")  

Next, we are going to append the planning subzone code from busstop_mpsz data frame onto odbus6_9 data frame.

Code

od_data <- left_join(odbus6_9 , busstop_mpsz,
            by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
  rename(ORIGIN_BS = ORIGIN_PT_CODE,
         ORIGIN_SZ = SUBZONE_C,
         DESTIN_BS = DESTINATION_PT_CODE)

Before continue, it is a good practice for us to check for duplicating records.

Code

duplicate <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()

If duplicated records are found, the code chunk below will be used to retain the unique records.

Code

od_data <- unique(od_data)

It will be a good practice to confirm if the duplicating records issue has been addressed fully.

Next, we will update od_data data frame cwith the planning subzone codes.

Code

od_data <- left_join(od_data , busstop_mpsz,
            by = c("DESTIN_BS" = "BUS_STOP_N")) 

Code

duplicate <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()

Code

od_data <- unique(od_data)

Code

od_data <- od_data %>%
  rename(DESTIN_SZ = SUBZONE_C) %>%
  drop_na() %>%
  group_by(ORIGIN_SZ, DESTIN_SZ) %>%
  summarise(MORNING_PEAK = sum(TRIPS))

It is time to save the output into an rds file format.

Code

write_rds(od_data, "data/rds/od_data_fii.rds")

Code

od_data_fii <- read_rds("data/rds/od_data_fii.rds")

6.0 Visualising Spatial Interaction

In this section, you will learn how to prepare a desire line by using stplanr package.

6.1 Removing intra-zonal flows

We will not plot the intra-zonal flows. The code chunk below will be used to remove intra-zonal flows.

Code

od_data_fij <- od_data[od_data$ORIGIN_SZ!=od_data$DESTIN_SZ,]

Code

write_rds(od_data_fij, "data/rds/od_data_fij.rds")

Code

od_data_fij <- read_rds("data/rds/od_data_fij.rds")

6.2 Creating desire lines

In this code chunk below, od2line() of stplanr package is used to create the desire lines.

Code

flowLine <- od2line(flow = od_data_fij, 
                    zones = mpsz,
                    zone_code = "SUBZONE_C")

Code

write_rds(flowLine, "data/rds/flowLine.rds")

Code

flowLine <- read_rds("data/rds/flowLine.rds")

6.3 Visualising the desire lines

To visualise the resulting desire lines, the code chunk below is used.

Code

tm_shape(mpsz) +
  tm_polygons() +
flowLine %>%  
tm_shape() +
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)

When the flow data are very messy and highly skewed like the one shown above, it is wiser to focus on selected flows, for example flow greater than or equal to 5000 as shown below.

Code

tm_shape(mpsz) +
  tm_polygons() +
flowLine %>%  
  filter(MORNING_PEAK >= 5000) %>%
tm_shape() +
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)

1.0 Overview

Spatial Interaction Models (SIMs) are mathematical models for estimating flows between spatial entities developed by Alan Wilson in the late 1960s and early 1970, with considerable uptake and refinement for transport modelling since then Boyce and Williams (2015).

There are four main types of traditional SIMs (Wilson 1971):

• Unconstrained

• Production-constrained

• Attraction-constrained

• Doubly-constrained

Ordinary least square (OLS), log-normal, Poisson and negative binomial (NB) regression methods have been used extensively to calibrate OD flow models by processing flow data as different types of dependent variables. In this chapter, you will gain hands-on experiences on using appropriate R packages to calibrate SIM by using there four regression methods.

2.0 The Data

This exercise is a continuation of Chapter 15: Processing and Visualising Flow Data and the following data will be used:

• od_data.rds, weekday morning peak passenger flows at planning subzone level.

• mpsz.rds, URA Master Plan 2019 Planning Subzone boundary in simple feature tibble data frame format.

Beside these two data sets, an additional attribute data file called pop.csv will be provided. It

3.0 Computing Distance Matrix

In spatial interaction, a distance matrix is a table that shows the distance between pairs of locations. For example, in the table below we can see an Euclidean distance of 3926.0025 between MESZ01 and RVSZ05, of 3939.1079 between MESZ01 and SRSZ01, and so on. By definition, an location’s distance from itself, which is shown in the main diagonal of the table, is 0.

In this section, you will learn how to compute a distance matrix by using URA Master Plan 2019 Planning Subzone boundary in which you saved as an rds file called mpsz.

First, let us import mpsz.rds into R environemnt by using the code chunk below.

Code

mpsz <- read_rds("data/rds/mpsz.rds")
mpsz

Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM
First 10 features:
                 SUBZONE_N SUBZONE_C       PLN_AREA_N PLN_AREA_C       REGION_N
1              MARINA EAST    MESZ01      MARINA EAST         ME CENTRAL REGION
2         INSTITUTION HILL    RVSZ05     RIVER VALLEY         RV CENTRAL REGION
3           ROBERTSON QUAY    SRSZ01  SINGAPORE RIVER         SR CENTRAL REGION
4  JURONG ISLAND AND BUKOM    WISZ01  WESTERN ISLANDS         WI    WEST REGION
5             FORT CANNING    MUSZ02           MUSEUM         MU CENTRAL REGION
6         MARINA EAST (MP)    MPSZ05    MARINE PARADE         MP CENTRAL REGION
7                   SUDONG    WISZ03  WESTERN ISLANDS         WI    WEST REGION
8                  SEMAKAU    WISZ02  WESTERN ISLANDS         WI    WEST REGION
9           SOUTHERN GROUP    SISZ02 SOUTHERN ISLANDS         SI CENTRAL REGION
10                 SENTOSA    SISZ01 SOUTHERN ISLANDS         SI CENTRAL REGION
   REGION_C                       geometry
1        CR MULTIPOLYGON (((33222.98 29...
2        CR MULTIPOLYGON (((28481.45 30...
3        CR MULTIPOLYGON (((28087.34 30...
4        WR MULTIPOLYGON (((14557.7 304...
5        CR MULTIPOLYGON (((29542.53 31...
6        CR MULTIPOLYGON (((35279.55 30...
7        WR MULTIPOLYGON (((15772.59 21...
8        WR MULTIPOLYGON (((19843.41 21...
9        CR MULTIPOLYGON (((30870.53 22...
10       CR MULTIPOLYGON (((26879.04 26...

Notice that it is a sf tibble dataframe object class.

3.1 Converting from sf data.table to SpatialPolygonsDataFrame

There are at least two ways to compute the required distance matrix. One is based on sf and the other is based on sp. Past experience shown that computing distance matrix by using sf function took relatively longer time that sp method especially the data set is large. In view of this, sp method is used in the code chunks below.

First as.Spatial() will be used to convert mpsz from sf tibble data frame to SpatialPolygonsDataFrame of sp object as shown in the code chunk below.

Code

mpsz_sp <- as(mpsz, "Spatial")
mpsz_sp

class       : SpatialPolygonsDataFrame 
features    : 332 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 6
names       : SUBZONE_N, SUBZONE_C, PLN_AREA_N, PLN_AREA_C,       REGION_N, REGION_C 
min values  : ADMIRALTY,    AMSZ01, ANG MO KIO,         AM, CENTRAL REGION,       CR 
max values  :    YUNNAN,    YSSZ09,     YISHUN,         YS,    WEST REGION,       WR 

3.2 Computing distance matrix

Next, spDists() of sp package will be used to compute the Euclidean distance between the centroids of the planning subzones.

Code

dist <- spDists(mpsz_sp, 
                longlat = FALSE)

Code

head(dist, n=c(10, 10))

           [,1]       [,2]      [,3]      [,4]       [,5]      [,6]      [,7]
 [1,]     0.000  3926.0025  3939.108 20252.964  2989.9839  1431.330 19211.836
 [2,]  3926.003     0.0000   305.737 16513.865   951.8314  5254.066 16242.523
 [3,]  3939.108   305.7370     0.000 16412.062  1045.9088  5299.849 16026.146
 [4,] 20252.964 16513.8648 16412.062     0.000 17450.3044 21665.795  7229.017
 [5,]  2989.984   951.8314  1045.909 17450.304     0.0000  4303.232 17020.916
 [6,]  1431.330  5254.0664  5299.849 21665.795  4303.2323     0.000 20617.082
 [7,] 19211.836 16242.5230 16026.146  7229.017 17020.9161 20617.082     0.000
 [8,] 14960.942 12749.4101 12477.871 11284.279 13336.0421 16281.453  5606.082
 [9,]  7515.256  7934.8082  7649.776 18427.503  7801.6163  8403.896 14810.930
[10,]  6391.342  4975.0021  4669.295 15469.566  5226.8731  7707.091 13111.391
           [,8]      [,9]     [,10]
 [1,] 14960.942  7515.256  6391.342
 [2,] 12749.410  7934.808  4975.002
 [3,] 12477.871  7649.776  4669.295
 [4,] 11284.279 18427.503 15469.566
 [5,] 13336.042  7801.616  5226.873
 [6,] 16281.453  8403.896  7707.091
 [7,]  5606.082 14810.930 13111.391
 [8,]     0.000  9472.024  8575.490
 [9,]  9472.024     0.000  3780.800
[10,]  8575.490  3780.800     0.000

Notice that the output dist is a matrix object class of R. Also notice that the column heanders and row headers are not labeled with the planning subzone codes.

3.3 Labelling column and row heanders of a distance matrix

First, we will create a list sorted according to the the distance matrix by planning sub-zone code.

Code

sz_names <- mpsz$SUBZONE_C

Next we will attach SUBZONE_C to row and column for distance matrix matching ahead

Code

colnames(dist) <- paste0(sz_names)
rownames(dist) <- paste0(sz_names)

3.4 Pivoting distance value by SUBZONE_C

Next, we will pivot the distance matrix into a long table by using the row and column subzone codes as show in the code chunk below.

Code

distPair <- melt(dist) %>%
  rename(dist = value)
head(distPair, 10)

     Var1   Var2      dist
1  MESZ01 MESZ01     0.000
2  RVSZ05 MESZ01  3926.003
3  SRSZ01 MESZ01  3939.108
4  WISZ01 MESZ01 20252.964
5  MUSZ02 MESZ01  2989.984
6  MPSZ05 MESZ01  1431.330
7  WISZ03 MESZ01 19211.836
8  WISZ02 MESZ01 14960.942
9  SISZ02 MESZ01  7515.256
10 SISZ01 MESZ01  6391.342

Notice that the within zone distance is 0.

3.5 Updating intra-zonal distances

In this section, we are going to append a constant value to replace the intra-zonal distance of 0.

First, we will select and find out the minimum value of the distance by using summary().

Code

distPair %>%
  filter(dist > 0) %>%
  summary()

      Var1             Var2             dist        
 MESZ01 :   331   MESZ01 :   331   Min.   :  173.8  
 RVSZ05 :   331   RVSZ05 :   331   1st Qu.: 7149.5  
 SRSZ01 :   331   SRSZ01 :   331   Median :11890.0  
 WISZ01 :   331   WISZ01 :   331   Mean   :12229.4  
 MUSZ02 :   331   MUSZ02 :   331   3rd Qu.:16401.7  
 MPSZ05 :   331   MPSZ05 :   331   Max.   :49894.4  
 (Other):107906   (Other):107906                    

Next, a constant distance value of 50m is added into intra-zones distance.

Code

distPair$dist <- ifelse(distPair$dist == 0,
                        50, distPair$dist)

The code chunk below will be used to check the result data.frame.

Code

distPair %>%
  summary()

      Var1             Var2             dist      
 MESZ01 :   332   MESZ01 :   332   Min.   :   50  
 RVSZ05 :   332   RVSZ05 :   332   1st Qu.: 7097  
 SRSZ01 :   332   SRSZ01 :   332   Median :11864  
 WISZ01 :   332   WISZ01 :   332   Mean   :12193  
 MUSZ02 :   332   MUSZ02 :   332   3rd Qu.:16388  
 MPSZ05 :   332   MPSZ05 :   332   Max.   :49894  
 (Other):108232   (Other):108232                  

The code chunk below is used to rename the origin and destination fields.

Code

distPair <- distPair %>%
  rename(orig = Var1,
         dest = Var2)

Lastly, the code chunk below is used to save the dataframe for future use.

Code

write_rds(distPair, "data/rds/distPair.rds") 

Code

distPair <- read_rds("data/rds/distPair.rds")

4.0 Preparing the Flow Data

The code chunk below is used import od_data save in Chapter 15 into R environment.

Code

od_data_fii <- read_rds("data/rds/od_data_fii.rds")

Next, we will compute the total passenger trip between and within planning subzones by using the code chunk below. The output is all flow_data.

Code

flow_data <- od_data_fii %>%
  group_by(ORIGIN_SZ, DESTIN_SZ) %>% 
  summarize(TRIPS = sum(MORNING_PEAK)) 

Use the code chunk below to display flow_data dataframe.

Code

head(flow_data, 10)

# A tibble: 10 × 3
# Groups:   ORIGIN_SZ [1]
   ORIGIN_SZ DESTIN_SZ TRIPS
   <chr>     <chr>     <dbl>
 1 AMSZ01    AMSZ01     1998
 2 AMSZ01    AMSZ02     8289
 3 AMSZ01    AMSZ03     8971
 4 AMSZ01    AMSZ04     2252
 5 AMSZ01    AMSZ05     6136
 6 AMSZ01    AMSZ06     2148
 7 AMSZ01    AMSZ07     1620
 8 AMSZ01    AMSZ08     1925
 9 AMSZ01    AMSZ09     1773
10 AMSZ01    AMSZ10       63

4.1 Separating intra-flow from passenger volume df

Code chunk below is used to add three new fields in flow_data dataframe.

Code

flow_data$FlowNoIntra <- ifelse(
  flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ, 
  0, flow_data$TRIPS)
flow_data$offset <- ifelse(
  flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ, 
  0.000001, 1)

4.2 Combining passenger volume data with distance value

Before we can join flow_data and distPair, we need to convert data value type of ORIGIN_SZ and DESTIN_SZ fields of flow_data dataframe into factor data type.

Code

flow_data$ORIGIN_SZ <- as.factor(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.factor(flow_data$DESTIN_SZ)

Now, left_join() of dplyr will be used to flow_data dataframe and distPair dataframe. The output is called flow_data1.

Code

flow_data1 <- flow_data %>%
  left_join (distPair,
             by = c("ORIGIN_SZ" = "orig",
                    "DESTIN_SZ" = "dest"))

5.0 Preparing Origin and Destination Attributes

5.1 Importing population data

Code

pop <- read_csv("data/aspatial/pop.csv")

5.2 Geospatial data wrangling

Code

pop <- pop %>%
  left_join(mpsz,
            by = c("PA" = "PLN_AREA_N",
                   "SZ" = "SUBZONE_N")) %>%
  select(1:6) %>%
  rename(SZ_NAME = SZ,
         SZ = SUBZONE_C)

5.3 Preparing origin attribute

Code

flow_data1 <- flow_data1 %>%
  left_join(pop,
            by = c(ORIGIN_SZ = "SZ")) %>%
  rename(ORIGIN_AGE7_12 = AGE7_12,
         ORIGIN_AGE13_24 = AGE13_24,
         ORIGIN_AGE25_64 = AGE25_64) %>%
  select(-c(PA, SZ_NAME))

5.4 Preparing destination attribute

Code

flow_data1 <- flow_data1 %>%
  left_join(pop,
            by = c(DESTIN_SZ = "SZ")) %>%
  rename(DESTIN_AGE7_12 = AGE7_12,
         DESTIN_AGE13_24 = AGE13_24,
         DESTIN_AGE25_64 = AGE25_64) %>%
  select(-c(PA, SZ_NAME))

We will called the output data file SIM_data. it is in rds data file format.

Code

write_rds(flow_data1, "data/rds/flow_data_6-9.rds")

6.0 Calibrating Spatial Interaction Models

In this section, you will learn how to calibrate Spatial Interaction Models by using Poisson Regression method.

6.1 Importing the modelling data

Firstly, let us import the modelling data by using the code chunk below.

Code

SIM_data <- read_rds("data/rds/flow_data_6-9.rds")

6.2 Visualising the dependent variable

Firstly, let us plot the distribution of the dependent variable (i.e. TRIPS) by using histogram method by using the code chunk below.

Code

ggplot(data = SIM_data,
       aes(x = TRIPS)) +
  geom_histogram()

Notice that the distribution is highly skewed and not resemble bell shape or also known as normal distribution.

Next, let us visualise the relation between the dependent variable and one of the key independent variable in Spatial Interaction Model, namely distance.

Code

ggplot(data = SIM_data,
       aes(x = dist,
           y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

Notice that their relationship hardly resemble linear relationship.

On the other hand, if we plot the scatter plot by using the log transformed version of both variables, we can see that their relationship is more resemble linear relationship.

Code

ggplot(data = SIM_data,
       aes(x = log(dist),
           y = log(TRIPS))) +
  geom_point() +
  geom_smooth(method = lm)

6.3 Checking for variables with zero values

Since Poisson Regression is based of log and log 0 is undefined, it is important for us to ensure that no 0 values in the explanatory variables.

In the code chunk below, summary() of Base R is used to compute the summary statistics of all variables in SIM_data data frame.

Code

summary(SIM_data)

  ORIGIN_SZ          DESTIN_SZ             TRIPS         FlowNoIntra      
 Length:14734       Length:14734       Min.   :     1   Min.   :     0.0  
 Class :character   Class :character   1st Qu.:    14   1st Qu.:    13.0  
 Mode  :character   Mode  :character   Median :    76   Median :    70.0  
                                       Mean   :  1021   Mean   :   839.9  
                                       3rd Qu.:   426   3rd Qu.:   379.0  
                                       Max.   :232187   Max.   :148274.0  
     offset              dist       ORIGIN_AGE7_12 ORIGIN_AGE13_24
 Min.   :0.000001   Min.   :   50   Min.   :   0   Min.   :    0  
 1st Qu.:1.000000   1st Qu.: 3346   1st Qu.: 240   1st Qu.:  440  
 Median :1.000000   Median : 6067   Median : 700   Median : 1350  
 Mean   :0.982150   Mean   : 6880   Mean   :1032   Mean   : 2269  
 3rd Qu.:1.000000   3rd Qu.: 9729   3rd Qu.:1480   3rd Qu.: 3260  
 Max.   :1.000000   Max.   :26136   Max.   :6340   Max.   :16380  
 ORIGIN_AGE25_64 DESTIN_AGE7_12 DESTIN_AGE13_24 DESTIN_AGE25_64
 Min.   :    0   Min.   :   0   Min.   :    0   Min.   :    0  
 1st Qu.: 2200   1st Qu.: 240   1st Qu.:  460   1st Qu.: 2200  
 Median : 6810   Median : 720   Median : 1420   Median : 7030  
 Mean   :10487   Mean   :1033   Mean   : 2290   Mean   :10574  
 3rd Qu.:15770   3rd Qu.:1500   3rd Qu.: 3260   3rd Qu.:15830  
 Max.   :74610   Max.   :6340   Max.   :16380   Max.   :74610  

The print report above reveals that variables ORIGIN_AGE7_12, ORIGIN_AGE13_24, ORIGIN_AGE25_64,DESTIN_AGE7_12, DESTIN_AGE13_24, DESTIN_AGE25_64 consist of 0 values.

In view of this, code chunk below will be used to replace zero values to 0.99.

Code

SIM_data$DESTIN_AGE7_12 <- ifelse(
  SIM_data$DESTIN_AGE7_12 == 0,
  0.99, SIM_data$DESTIN_AGE7_12)
SIM_data$DESTIN_AGE13_24 <- ifelse(
  SIM_data$DESTIN_AGE13_24 == 0,
  0.99, SIM_data$DESTIN_AGE13_24)
SIM_data$DESTIN_AGE25_64 <- ifelse(
  SIM_data$DESTIN_AGE25_64 == 0,
  0.99, SIM_data$DESTIN_AGE25_64)
SIM_data$ORIGIN_AGE7_12 <- ifelse(
  SIM_data$ORIGIN_AGE7_12 == 0,
  0.99, SIM_data$ORIGIN_AGE7_12)
SIM_data$ORIGIN_AGE13_24 <- ifelse(
  SIM_data$ORIGIN_AGE13_24 == 0,
  0.99, SIM_data$ORIGIN_AGE13_24)
SIM_data$ORIGIN_AGE25_64 <- ifelse(
  SIM_data$ORIGIN_AGE25_64 == 0,
  0.99, SIM_data$ORIGIN_AGE25_64)

You can run the summary() again.

Code

summary(SIM_data)

  ORIGIN_SZ          DESTIN_SZ             TRIPS         FlowNoIntra      
 Length:14734       Length:14734       Min.   :     1   Min.   :     0.0  
 Class :character   Class :character   1st Qu.:    14   1st Qu.:    13.0  
 Mode  :character   Mode  :character   Median :    76   Median :    70.0  
                                       Mean   :  1021   Mean   :   839.9  
                                       3rd Qu.:   426   3rd Qu.:   379.0  
                                       Max.   :232187   Max.   :148274.0  
     offset              dist       ORIGIN_AGE7_12    ORIGIN_AGE13_24   
 Min.   :0.000001   Min.   :   50   Min.   :   0.99   Min.   :    0.99  
 1st Qu.:1.000000   1st Qu.: 3346   1st Qu.: 240.00   1st Qu.:  440.00  
 Median :1.000000   Median : 6067   Median : 700.00   Median : 1350.00  
 Mean   :0.982150   Mean   : 6880   Mean   :1031.86   Mean   : 2268.84  
 3rd Qu.:1.000000   3rd Qu.: 9729   3rd Qu.:1480.00   3rd Qu.: 3260.00  
 Max.   :1.000000   Max.   :26136   Max.   :6340.00   Max.   :16380.00  
 ORIGIN_AGE25_64    DESTIN_AGE7_12    DESTIN_AGE13_24    DESTIN_AGE25_64   
 Min.   :    0.99   Min.   :   0.99   Min.   :    0.99   Min.   :    0.99  
 1st Qu.: 2200.00   1st Qu.: 240.00   1st Qu.:  460.00   1st Qu.: 2200.00  
 Median : 6810.00   Median : 720.00   Median : 1420.00   Median : 7030.00  
 Mean   :10487.62   Mean   :1033.40   Mean   : 2290.35   Mean   :10574.46  
 3rd Qu.:15770.00   3rd Qu.:1500.00   3rd Qu.: 3260.00   3rd Qu.:15830.00  
 Max.   :74610.00   Max.   :6340.00   Max.   :16380.00   Max.   :74610.00  

Notice that all the 0 values have been replaced by 0.99.

6.4 Unconstrained Spatial Interaction Model

In this section, you will learn how to calibrate an unconstrained spatial interaction model by using glm() of Base Stats. The explanatory variables are origin population by different age cohort, destination population by different age cohort (i.e. ORIGIN_AGE25_64) and distance between origin and destination in km (i.e. dist).

The code chunk used to calibrate to model is shown below:

Code

uncSIM <- glm(formula = TRIPS ~ 
                log(ORIGIN_AGE25_64) + 
                log(DESTIN_AGE25_64) +
                log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
uncSIM

Call:  glm(formula = TRIPS ~ log(ORIGIN_AGE25_64) + log(DESTIN_AGE25_64) + 
    log(dist), family = poisson(link = "log"), data = SIM_data, 
    na.action = na.exclude)

Coefficients:
         (Intercept)  log(ORIGIN_AGE25_64)  log(DESTIN_AGE25_64)  
           10.407308              0.244859              0.009562  
           log(dist)  
           -0.705896  

Degrees of Freedom: 14733 Total (i.e. Null);  14730 Residual
Null Deviance:      60800000 
Residual Deviance: 36430000     AIC: 36520000

6.5 R-squared function

In order to measure how much variation of the trips can be accounted by the model we will write a function to calculate R-Squared value as shown below.

Code

CalcRSquared <- function(observed,estimated){
  r <- cor(observed,estimated)
  R2 <- r^2
  R2
}

Next, we will compute the R-squared of the unconstrained SIM by using the code chunk below.

Code

CalcRSquared(uncSIM$data$TRIPS, uncSIM$fitted.values)

[1] 0.1892576

Code

r2_mcfadden(uncSIM)

# R2 for Generalized Linear Regression
       R2: 0.400
  adj. R2: 0.400

6.6 Origin (Production) constrained SIM

In this section, we will fit an origin constrained SIM by using the code3 chunk below.

The general formula of Origin Constrained Spatial Interaction Model

Code

orcSIM <- glm(formula = TRIPS ~ 
                 ORIGIN_SZ +
                 log(DESTIN_AGE25_64) +
                 log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
summary(orcSIM)

Call:
glm(formula = TRIPS ~ ORIGIN_SZ + log(DESTIN_AGE25_64) + log(dist), 
    family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)

Coefficients:
                       Estimate Std. Error   z value Pr(>|z|)    
(Intercept)           1.211e+01  3.785e-03  3199.012  < 2e-16 ***
ORIGIN_SZAMSZ02       1.008e+00  4.450e-03   226.401  < 2e-16 ***
ORIGIN_SZAMSZ03       5.474e-01  4.563e-03   119.959  < 2e-16 ***
ORIGIN_SZAMSZ04      -7.494e-02  5.187e-03   -14.448  < 2e-16 ***
ORIGIN_SZAMSZ05      -2.006e-01  5.790e-03   -34.650  < 2e-16 ***
ORIGIN_SZAMSZ06       4.193e-01  5.130e-03    81.736  < 2e-16 ***
ORIGIN_SZAMSZ07      -1.372e+00  9.683e-03  -141.686  < 2e-16 ***
ORIGIN_SZAMSZ08      -1.022e+00  8.956e-03  -114.087  < 2e-16 ***
ORIGIN_SZAMSZ09       2.239e-01  5.408e-03    41.396  < 2e-16 ***
ORIGIN_SZAMSZ10       5.061e-01  4.716e-03   107.311  < 2e-16 ***
ORIGIN_SZAMSZ11      -1.856e+00  1.285e-02  -144.414  < 2e-16 ***
ORIGIN_SZAMSZ12      -1.580e+00  1.076e-02  -146.883  < 2e-16 ***
ORIGIN_SZBDSZ01       1.072e+00  4.345e-03   246.734  < 2e-16 ***
ORIGIN_SZBDSZ02       5.198e-01  5.079e-03   102.340  < 2e-16 ***
ORIGIN_SZBDSZ03       9.865e-01  4.490e-03   219.724  < 2e-16 ***
ORIGIN_SZBDSZ04       1.767e+00  3.894e-03   453.646  < 2e-16 ***
ORIGIN_SZBDSZ05       6.395e-01  4.546e-03   140.691  < 2e-16 ***
ORIGIN_SZBDSZ06       9.363e-01  4.543e-03   206.094  < 2e-16 ***
ORIGIN_SZBDSZ07      -1.281e+00  9.558e-03  -133.991  < 2e-16 ***
ORIGIN_SZBDSZ08      -1.167e+00  9.032e-03  -129.194  < 2e-16 ***
ORIGIN_SZBKSZ01      -4.540e-01  6.538e-03   -69.437  < 2e-16 ***
ORIGIN_SZBKSZ02       3.736e-01  5.115e-03    73.050  < 2e-16 ***
ORIGIN_SZBKSZ03       5.841e-01  4.934e-03   118.375  < 2e-16 ***
ORIGIN_SZBKSZ04      -1.177e-01  5.914e-03   -19.895  < 2e-16 ***
ORIGIN_SZBKSZ05      -2.164e-01  5.832e-03   -37.115  < 2e-16 ***
ORIGIN_SZBKSZ06       3.684e-03  5.873e-03     0.627  0.53048    
ORIGIN_SZBKSZ07       7.456e-01  4.426e-03   168.439  < 2e-16 ***
ORIGIN_SZBKSZ08      -2.279e-02  5.348e-03    -4.261 2.04e-05 ***
ORIGIN_SZBKSZ09      -9.572e-02  5.721e-03   -16.733  < 2e-16 ***
ORIGIN_SZBLSZ01      -1.688e+00  1.482e-02  -113.887  < 2e-16 ***
ORIGIN_SZBLSZ02      -2.154e+00  1.924e-02  -111.980  < 2e-16 ***
ORIGIN_SZBLSZ03      -3.249e+00  3.930e-02   -82.662  < 2e-16 ***
ORIGIN_SZBLSZ04      -2.203e+00  2.306e-02   -95.557  < 2e-16 ***
ORIGIN_SZBMSZ01      -1.267e-01  5.222e-03   -24.266  < 2e-16 ***
ORIGIN_SZBMSZ02      -1.075e+00  6.742e-03  -159.386  < 2e-16 ***
ORIGIN_SZBMSZ03      -4.386e-01  5.794e-03   -75.707  < 2e-16 ***
ORIGIN_SZBMSZ04      -6.333e-02  5.157e-03   -12.280  < 2e-16 ***
ORIGIN_SZBMSZ05      -2.256e+00  1.247e-02  -180.957  < 2e-16 ***
ORIGIN_SZBMSZ06      -2.378e+00  1.618e-02  -147.029  < 2e-16 ***
ORIGIN_SZBMSZ07      -4.769e-01  5.653e-03   -84.362  < 2e-16 ***
ORIGIN_SZBMSZ08      -5.652e-01  5.811e-03   -97.259  < 2e-16 ***
ORIGIN_SZBMSZ09      -1.232e+00  8.688e-03  -141.760  < 2e-16 ***
ORIGIN_SZBMSZ10      -1.471e+00  9.130e-03  -161.131  < 2e-16 ***
ORIGIN_SZBMSZ11      -7.866e-01  6.595e-03  -119.263  < 2e-16 ***
ORIGIN_SZBMSZ12      -1.072e+00  9.149e-03  -117.206  < 2e-16 ***
ORIGIN_SZBMSZ13      -1.207e-01  5.691e-03   -21.218  < 2e-16 ***
ORIGIN_SZBMSZ14      -5.376e-01  6.629e-03   -81.098  < 2e-16 ***
ORIGIN_SZBMSZ15      -3.253e-01  6.054e-03   -53.740  < 2e-16 ***
ORIGIN_SZBMSZ16      -1.548e+00  9.144e-03  -169.303  < 2e-16 ***
ORIGIN_SZBMSZ17      -2.169e+00  1.576e-02  -137.622  < 2e-16 ***
ORIGIN_SZBPSZ01       1.369e-01  5.553e-03    24.660  < 2e-16 ***
ORIGIN_SZBPSZ02      -3.292e-02  6.462e-03    -5.094 3.50e-07 ***
ORIGIN_SZBPSZ03       1.491e-01  6.149e-03    24.241  < 2e-16 ***
ORIGIN_SZBPSZ04       3.544e-01  5.084e-03    69.711  < 2e-16 ***
ORIGIN_SZBPSZ05       5.454e-01  4.554e-03   119.764  < 2e-16 ***
ORIGIN_SZBPSZ06      -1.406e+00  9.311e-03  -151.045  < 2e-16 ***
ORIGIN_SZBPSZ07      -1.004e+00  8.575e-03  -117.068  < 2e-16 ***
ORIGIN_SZBSSZ01      -1.625e-02  5.276e-03    -3.080  0.00207 ** 
ORIGIN_SZBSSZ02       3.088e-01  4.787e-03    64.495  < 2e-16 ***
ORIGIN_SZBSSZ03       2.555e-01  4.689e-03    54.487  < 2e-16 ***
ORIGIN_SZBTSZ01      -6.646e-02  5.385e-03   -12.340  < 2e-16 ***
ORIGIN_SZBTSZ02      -1.078e+00  7.797e-03  -138.225  < 2e-16 ***
ORIGIN_SZBTSZ03      -2.284e-01  5.727e-03   -39.876  < 2e-16 ***
ORIGIN_SZBTSZ04      -1.053e+00  1.019e-02  -103.339  < 2e-16 ***
ORIGIN_SZBTSZ05      -1.647e+00  1.100e-02  -149.690  < 2e-16 ***
ORIGIN_SZBTSZ06      -7.804e-01  7.181e-03  -108.682  < 2e-16 ***
ORIGIN_SZBTSZ07      -2.298e+00  1.321e-02  -173.921  < 2e-16 ***
ORIGIN_SZBTSZ08      -1.283e+00  9.394e-03  -136.560  < 2e-16 ***
ORIGIN_SZCBSZ01      -1.911e+00  5.483e-02   -34.844  < 2e-16 ***
ORIGIN_SZCCSZ01      -1.758e+00  1.331e-02  -132.099  < 2e-16 ***
ORIGIN_SZCHSZ01      -1.236e+00  1.178e-02  -104.954  < 2e-16 ***
ORIGIN_SZCHSZ02      -5.424e-01  7.940e-03   -68.307  < 2e-16 ***
ORIGIN_SZCHSZ03       4.332e-01  5.841e-03    74.153  < 2e-16 ***
ORIGIN_SZCKSZ01       1.843e-01  5.117e-03    36.007  < 2e-16 ***
ORIGIN_SZCKSZ02       6.800e-01  5.087e-03   133.672  < 2e-16 ***
ORIGIN_SZCKSZ03       8.030e-01  4.522e-03   177.574  < 2e-16 ***
ORIGIN_SZCKSZ04       1.298e+00  4.562e-03   284.446  < 2e-16 ***
ORIGIN_SZCKSZ05       1.011e+00  5.305e-03   190.602  < 2e-16 ***
ORIGIN_SZCKSZ06       1.262e+00  5.042e-03   250.262  < 2e-16 ***
ORIGIN_SZCLSZ01      -6.805e-01  7.661e-03   -88.836  < 2e-16 ***
ORIGIN_SZCLSZ02      -1.837e+00  1.364e-02  -134.665  < 2e-16 ***
ORIGIN_SZCLSZ03      -1.001e+00  7.949e-03  -125.969  < 2e-16 ***
ORIGIN_SZCLSZ04       6.966e-01  4.460e-03   156.204  < 2e-16 ***
ORIGIN_SZCLSZ05      -1.974e+00  1.474e-02  -133.906  < 2e-16 ***
ORIGIN_SZCLSZ06       8.585e-01  4.204e-03   204.230  < 2e-16 ***
ORIGIN_SZCLSZ07      -2.974e-01  5.575e-03   -53.346  < 2e-16 ***
ORIGIN_SZCLSZ08       3.231e-01  5.802e-03    55.688  < 2e-16 ***
ORIGIN_SZCLSZ09      -1.697e+00  1.555e-02  -109.106  < 2e-16 ***
ORIGIN_SZDTSZ02      -4.061e+00  8.341e-02   -48.693  < 2e-16 ***
ORIGIN_SZDTSZ03      -4.031e+00  7.381e-02   -54.618  < 2e-16 ***
ORIGIN_SZDTSZ13      -3.000e+00  3.129e-02   -95.889  < 2e-16 ***
ORIGIN_SZGLSZ01      -1.405e+00  9.192e-03  -152.876  < 2e-16 ***
ORIGIN_SZGLSZ02       2.536e-01  4.889e-03    51.880  < 2e-16 ***
ORIGIN_SZGLSZ03       2.411e-01  4.855e-03    49.649  < 2e-16 ***
ORIGIN_SZGLSZ04       8.350e-01  4.200e-03   198.826  < 2e-16 ***
ORIGIN_SZGLSZ05       6.207e-01  4.375e-03   141.857  < 2e-16 ***
ORIGIN_SZHGSZ01       2.806e-01  4.746e-03    59.121  < 2e-16 ***
ORIGIN_SZHGSZ02       4.917e-01  4.712e-03   104.351  < 2e-16 ***
ORIGIN_SZHGSZ03       2.452e-01  5.113e-03    47.952  < 2e-16 ***
ORIGIN_SZHGSZ04       9.052e-01  4.303e-03   210.358  < 2e-16 ***
ORIGIN_SZHGSZ05       1.170e+00  4.253e-03   275.033  < 2e-16 ***
ORIGIN_SZHGSZ06      -1.016e-01  5.413e-03   -18.773  < 2e-16 ***
ORIGIN_SZHGSZ07       6.984e-01  4.455e-03   156.757  < 2e-16 ***
ORIGIN_SZHGSZ08       1.005e-01  5.354e-03    18.781  < 2e-16 ***
ORIGIN_SZHGSZ09      -5.390e-01  6.962e-03   -77.417  < 2e-16 ***
ORIGIN_SZHGSZ10      -3.512e+00  4.211e-02   -83.388  < 2e-16 ***
ORIGIN_SZJESZ01       4.022e-01  4.869e-03    82.601  < 2e-16 ***
ORIGIN_SZJESZ02       2.273e-01  4.924e-03    46.158  < 2e-16 ***
ORIGIN_SZJESZ03       1.829e-01  5.286e-03    34.598  < 2e-16 ***
ORIGIN_SZJESZ04      -1.177e+00  9.142e-03  -128.767  < 2e-16 ***
ORIGIN_SZJESZ05      -2.065e+00  1.382e-02  -149.494  < 2e-16 ***
ORIGIN_SZJESZ06       2.301e-01  4.853e-03    47.410  < 2e-16 ***
ORIGIN_SZJESZ07      -1.889e+00  1.183e-02  -159.599  < 2e-16 ***
ORIGIN_SZJESZ08      -1.062e+00  1.147e-02   -92.551  < 2e-16 ***
ORIGIN_SZJESZ09       5.237e-01  4.959e-03   105.612  < 2e-16 ***
ORIGIN_SZJESZ10      -1.829e+00  1.800e-02  -101.616  < 2e-16 ***
ORIGIN_SZJESZ11      -2.023e+00  1.931e-02  -104.738  < 2e-16 ***
ORIGIN_SZJWSZ01       2.125e-01  6.405e-03    33.183  < 2e-16 ***
ORIGIN_SZJWSZ02       8.858e-01  4.521e-03   195.929  < 2e-16 ***
ORIGIN_SZJWSZ03       1.269e+00  4.188e-03   302.922  < 2e-16 ***
ORIGIN_SZJWSZ04       1.284e+00  4.280e-03   300.017  < 2e-16 ***
ORIGIN_SZJWSZ05      -1.393e+00  1.252e-02  -111.339  < 2e-16 ***
ORIGIN_SZJWSZ06      -1.015e+00  1.067e-02   -95.109  < 2e-16 ***
ORIGIN_SZJWSZ07      -2.694e+00  2.751e-02   -97.911  < 2e-16 ***
ORIGIN_SZJWSZ08       1.950e+00  4.110e-03   474.430  < 2e-16 ***
ORIGIN_SZJWSZ09       1.831e+00  3.899e-03   469.595  < 2e-16 ***
ORIGIN_SZKLSZ01       1.636e-01  4.902e-03    33.374  < 2e-16 ***
ORIGIN_SZKLSZ02      -5.156e-01  6.321e-03   -81.570  < 2e-16 ***
ORIGIN_SZKLSZ03      -4.145e-01  5.949e-03   -69.666  < 2e-16 ***
ORIGIN_SZKLSZ04      -2.283e+00  1.187e-02  -192.327  < 2e-16 ***
ORIGIN_SZKLSZ05      -8.593e-01  8.272e-03  -103.882  < 2e-16 ***
ORIGIN_SZKLSZ06      -4.709e+00  1.857e-01   -25.352  < 2e-16 ***
ORIGIN_SZKLSZ07      -1.123e+00  8.408e-03  -133.615  < 2e-16 ***
ORIGIN_SZKLSZ08      -1.476e+00  9.152e-03  -161.321  < 2e-16 ***
ORIGIN_SZLKSZ01      -3.273e+00  3.875e-02   -84.465  < 2e-16 ***
ORIGIN_SZMDSZ01      -2.615e+00  2.802e-02   -93.303  < 2e-16 ***
ORIGIN_SZMDSZ02      -8.945e-01  1.035e-02   -86.389  < 2e-16 ***
ORIGIN_SZMDSZ03      -1.998e+00  1.703e-02  -117.297  < 2e-16 ***
ORIGIN_SZMPSZ01      -1.093e+00  8.367e-03  -130.656  < 2e-16 ***
ORIGIN_SZMPSZ02      -5.975e-01  6.898e-03   -86.616  < 2e-16 ***
ORIGIN_SZMPSZ03      -9.706e-03  5.319e-03    -1.825  0.06804 .  
ORIGIN_SZMUSZ02      -3.923e+00  1.038e-01   -37.806  < 2e-16 ***
ORIGIN_SZNTSZ01      -2.829e+00  3.529e-02   -80.157  < 2e-16 ***
ORIGIN_SZNTSZ02      -3.256e+00  2.323e-02  -140.180  < 2e-16 ***
ORIGIN_SZNTSZ03      -9.865e-01  7.777e-03  -126.848  < 2e-16 ***
ORIGIN_SZNTSZ05      -3.353e+00  4.964e-02   -67.546  < 2e-16 ***
ORIGIN_SZNTSZ06      -3.818e+00  5.576e-02   -68.483  < 2e-16 ***
ORIGIN_SZNVSZ01       4.449e-01  4.482e-03    99.269  < 2e-16 ***
ORIGIN_SZNVSZ02      -6.279e-01  6.470e-03   -97.044  < 2e-16 ***
ORIGIN_SZNVSZ03      -1.212e+00  7.788e-03  -155.644  < 2e-16 ***
ORIGIN_SZNVSZ04      -1.469e+00  9.091e-03  -161.543  < 2e-16 ***
ORIGIN_SZNVSZ05      -2.628e+00  1.579e-02  -166.466  < 2e-16 ***
ORIGIN_SZPGSZ01      -9.541e-01  1.223e-02   -78.035  < 2e-16 ***
ORIGIN_SZPGSZ02      -5.353e-01  7.233e-03   -74.009  < 2e-16 ***
ORIGIN_SZPGSZ03       9.574e-01  4.437e-03   215.779  < 2e-16 ***
ORIGIN_SZPGSZ04       1.110e+00  4.417e-03   251.169  < 2e-16 ***
ORIGIN_SZPGSZ05       2.658e-01  5.758e-03    46.156  < 2e-16 ***
ORIGIN_SZPLSZ01      -8.153e-01  1.044e-02   -78.119  < 2e-16 ***
ORIGIN_SZPLSZ02      -1.675e+00  1.478e-02  -113.340  < 2e-16 ***
ORIGIN_SZPLSZ03      -2.963e+00  3.672e-02   -80.686  < 2e-16 ***
ORIGIN_SZPLSZ04      -3.279e+00  3.684e-02   -89.012  < 2e-16 ***
ORIGIN_SZPLSZ05      -2.466e+00  2.245e-02  -109.864  < 2e-16 ***
ORIGIN_SZPNSZ01       1.411e+00  4.584e-03   307.690  < 2e-16 ***
ORIGIN_SZPNSZ02      -5.043e-01  1.108e-02   -45.503  < 2e-16 ***
ORIGIN_SZPNSZ03      -1.878e+00  1.940e-02   -96.796  < 2e-16 ***
ORIGIN_SZPNSZ04      -2.761e+00  3.112e-02   -88.706  < 2e-16 ***
ORIGIN_SZPNSZ05      -2.277e+00  2.628e-02   -86.662  < 2e-16 ***
ORIGIN_SZPRSZ01      -7.934e-01  1.142e-02   -69.499  < 2e-16 ***
ORIGIN_SZPRSZ02       9.414e-01  4.615e-03   203.981  < 2e-16 ***
ORIGIN_SZPRSZ03       7.674e-01  4.626e-03   165.881  < 2e-16 ***
ORIGIN_SZPRSZ04      -3.771e-01  7.516e-03   -50.168  < 2e-16 ***
ORIGIN_SZPRSZ05       1.327e+00  4.325e-03   306.737  < 2e-16 ***
ORIGIN_SZPRSZ06      -4.081e-01  8.651e-03   -47.172  < 2e-16 ***
ORIGIN_SZPRSZ07      -2.151e+00  1.610e-02  -133.558  < 2e-16 ***
ORIGIN_SZPRSZ08       5.293e-04  6.383e-03     0.083  0.93391    
ORIGIN_SZQTSZ01      -4.144e-01  6.846e-03   -60.539  < 2e-16 ***
ORIGIN_SZQTSZ02      -7.967e-01  6.327e-03  -125.933  < 2e-16 ***
ORIGIN_SZQTSZ03      -2.415e-01  5.681e-03   -42.509  < 2e-16 ***
ORIGIN_SZQTSZ04      -1.013e+00  7.129e-03  -142.123  < 2e-16 ***
ORIGIN_SZQTSZ05      -3.923e-01  5.994e-03   -65.446  < 2e-16 ***
ORIGIN_SZQTSZ06      -5.662e-01  6.481e-03   -87.359  < 2e-16 ***
ORIGIN_SZQTSZ07      -1.558e+00  9.635e-03  -161.662  < 2e-16 ***
ORIGIN_SZQTSZ08      -1.577e-01  5.699e-03   -27.665  < 2e-16 ***
ORIGIN_SZQTSZ09      -6.189e-01  6.633e-03   -93.312  < 2e-16 ***
ORIGIN_SZQTSZ10      -4.511e-01  6.512e-03   -69.271  < 2e-16 ***
ORIGIN_SZQTSZ11      -1.455e+00  9.800e-03  -148.421  < 2e-16 ***
ORIGIN_SZQTSZ12      -1.475e+00  1.044e-02  -141.309  < 2e-16 ***
ORIGIN_SZQTSZ13      -3.529e-01  6.413e-03   -55.038  < 2e-16 ***
ORIGIN_SZQTSZ14      -1.591e+00  9.847e-03  -161.565  < 2e-16 ***
ORIGIN_SZQTSZ15      -8.955e-01  1.027e-02   -87.184  < 2e-16 ***
ORIGIN_SZRCSZ01      -1.375e+00  1.265e-02  -108.704  < 2e-16 ***
ORIGIN_SZRCSZ06      -6.196e-01  8.475e-03   -73.116  < 2e-16 ***
ORIGIN_SZRVSZ01      -3.523e+00  3.237e-02  -108.818  < 2e-16 ***
ORIGIN_SZRVSZ02      -2.912e+00  2.776e-02  -104.868  < 2e-16 ***
ORIGIN_SZRVSZ03      -3.145e+00  2.379e-02  -132.232  < 2e-16 ***
ORIGIN_SZRVSZ04      -3.357e+00  5.567e-02   -60.309  < 2e-16 ***
ORIGIN_SZRVSZ05      -2.438e+00  1.644e-02  -148.272  < 2e-16 ***
ORIGIN_SZSBSZ01       5.890e-01  5.529e-03   106.520  < 2e-16 ***
ORIGIN_SZSBSZ02      -7.098e-01  8.213e-03   -86.432  < 2e-16 ***
ORIGIN_SZSBSZ03       9.634e-01  4.611e-03   208.943  < 2e-16 ***
ORIGIN_SZSBSZ04       7.729e-01  5.289e-03   146.136  < 2e-16 ***
ORIGIN_SZSBSZ05      -9.966e-02  6.543e-03   -15.231  < 2e-16 ***
ORIGIN_SZSBSZ06      -1.778e+00  1.719e-02  -103.427  < 2e-16 ***
ORIGIN_SZSBSZ07      -1.161e+00  1.256e-02   -92.436  < 2e-16 ***
ORIGIN_SZSBSZ08      -1.212e+00  1.222e-02   -99.227  < 2e-16 ***
ORIGIN_SZSBSZ09      -5.783e-01  8.579e-03   -67.412  < 2e-16 ***
ORIGIN_SZSESZ02       9.999e-01  4.409e-03   226.798  < 2e-16 ***
ORIGIN_SZSESZ03       1.214e+00  4.164e-03   291.675  < 2e-16 ***
ORIGIN_SZSESZ04       8.141e-01  4.868e-03   167.238  < 2e-16 ***
ORIGIN_SZSESZ05      -2.186e-01  5.915e-03   -36.961  < 2e-16 ***
ORIGIN_SZSESZ06       7.298e-01  4.689e-03   155.641  < 2e-16 ***
ORIGIN_SZSESZ07      -2.543e+00  1.961e-02  -129.689  < 2e-16 ***
ORIGIN_SZSGSZ01      -1.016e+00  8.550e-03  -118.869  < 2e-16 ***
ORIGIN_SZSGSZ02      -1.120e+00  9.589e-03  -116.799  < 2e-16 ***
ORIGIN_SZSGSZ03       2.169e-01  5.167e-03    41.970  < 2e-16 ***
ORIGIN_SZSGSZ04       2.672e-01  4.792e-03    55.757  < 2e-16 ***
ORIGIN_SZSGSZ05      -1.785e+00  1.060e-02  -168.456  < 2e-16 ***
ORIGIN_SZSGSZ06       4.017e-01  4.541e-03    88.470  < 2e-16 ***
ORIGIN_SZSGSZ07      -6.303e-01  6.235e-03  -101.098  < 2e-16 ***
ORIGIN_SZSKSZ01      -1.928e-01  7.765e-03   -24.826  < 2e-16 ***
ORIGIN_SZSKSZ02       3.870e-01  5.689e-03    68.026  < 2e-16 ***
ORIGIN_SZSKSZ03      -6.815e-01  7.983e-03   -85.369  < 2e-16 ***
ORIGIN_SZSKSZ04      -2.528e+00  2.702e-02   -93.548  < 2e-16 ***
ORIGIN_SZSKSZ05      -1.370e+00  1.552e-02   -88.311  < 2e-16 ***
ORIGIN_SZSLSZ01      -3.218e+00  3.058e-02  -105.238  < 2e-16 ***
ORIGIN_SZSLSZ04      -6.800e-01  7.683e-03   -88.497  < 2e-16 ***
ORIGIN_SZSRSZ01      -2.389e+00  1.583e-02  -150.989  < 2e-16 ***
ORIGIN_SZTHSZ01      -2.183e+00  4.887e-02   -44.666  < 2e-16 ***
ORIGIN_SZTHSZ03      -2.243e+00  2.243e-02  -100.025  < 2e-16 ***
ORIGIN_SZTHSZ04      -2.005e+00  2.869e-02   -69.879  < 2e-16 ***
ORIGIN_SZTHSZ06      -2.276e+00  1.784e-02  -127.557  < 2e-16 ***
ORIGIN_SZTMSZ01       4.015e-01  5.814e-03    69.048  < 2e-16 ***
ORIGIN_SZTMSZ02       2.222e+00  3.795e-03   585.568  < 2e-16 ***
ORIGIN_SZTMSZ03       1.412e+00  4.108e-03   343.608  < 2e-16 ***
ORIGIN_SZTMSZ04       9.106e-01  4.742e-03   192.036  < 2e-16 ***
ORIGIN_SZTMSZ05      -3.259e-01  7.534e-03   -43.253  < 2e-16 ***
ORIGIN_SZTNSZ01      -1.806e+00  1.038e-02  -174.076  < 2e-16 ***
ORIGIN_SZTNSZ02      -1.741e+00  9.778e-03  -178.108  < 2e-16 ***
ORIGIN_SZTNSZ03      -2.277e+00  1.338e-02  -170.199  < 2e-16 ***
ORIGIN_SZTNSZ04      -7.703e-01  7.197e-03  -107.032  < 2e-16 ***
ORIGIN_SZTPSZ01      -6.466e-01  6.287e-03  -102.841  < 2e-16 ***
ORIGIN_SZTPSZ02       4.633e-01  4.347e-03   106.578  < 2e-16 ***
ORIGIN_SZTPSZ03      -5.186e-01  6.085e-03   -85.234  < 2e-16 ***
ORIGIN_SZTPSZ04      -2.900e-01  5.779e-03   -50.190  < 2e-16 ***
ORIGIN_SZTPSZ05      -2.169e-01  6.072e-03   -35.720  < 2e-16 ***
ORIGIN_SZTPSZ06       3.357e-01  5.942e-03    56.486  < 2e-16 ***
ORIGIN_SZTPSZ07      -2.517e-01  6.317e-03   -39.846  < 2e-16 ***
ORIGIN_SZTPSZ08      -1.075e+00  9.109e-03  -118.034  < 2e-16 ***
ORIGIN_SZTPSZ09      -3.708e-01  6.189e-03   -59.903  < 2e-16 ***
ORIGIN_SZTPSZ10      -6.889e-01  7.634e-03   -90.229  < 2e-16 ***
ORIGIN_SZTPSZ11       7.661e-02  5.459e-03    14.033  < 2e-16 ***
ORIGIN_SZTPSZ12      -5.971e-01  6.522e-03   -91.552  < 2e-16 ***
ORIGIN_SZTSSZ01      -3.517e+00  4.739e-02   -74.210  < 2e-16 ***
ORIGIN_SZTSSZ02       3.022e-01  7.334e-03    41.203  < 2e-16 ***
ORIGIN_SZTSSZ03       3.730e-01  7.073e-03    52.733  < 2e-16 ***
ORIGIN_SZTSSZ04       3.610e-01  7.463e-03    48.372  < 2e-16 ***
ORIGIN_SZTSSZ05      -1.103e+00  1.404e-02   -78.566  < 2e-16 ***
ORIGIN_SZTSSZ06      -1.310e+00  1.718e-02   -76.286  < 2e-16 ***
ORIGIN_SZWCSZ01      -1.233e-01  7.861e-03   -15.690  < 2e-16 ***
ORIGIN_SZWCSZ02      -2.872e+00  3.159e-02   -90.911  < 2e-16 ***
ORIGIN_SZWCSZ03      -4.138e+00  1.241e-01   -33.349  < 2e-16 ***
ORIGIN_SZWDSZ01       1.370e+00  4.146e-03   330.448  < 2e-16 ***
ORIGIN_SZWDSZ02       1.041e+00  4.747e-03   219.219  < 2e-16 ***
ORIGIN_SZWDSZ03       2.189e+00  4.035e-03   542.344  < 2e-16 ***
ORIGIN_SZWDSZ04       1.142e+00  4.963e-03   230.074  < 2e-16 ***
ORIGIN_SZWDSZ05       5.160e-01  4.998e-03   103.230  < 2e-16 ***
ORIGIN_SZWDSZ06       1.208e+00  4.611e-03   262.019  < 2e-16 ***
ORIGIN_SZWDSZ07      -3.805e-01  8.034e-03   -47.365  < 2e-16 ***
ORIGIN_SZWDSZ08      -4.839e-01  7.878e-03   -61.426  < 2e-16 ***
ORIGIN_SZWDSZ09       1.475e+00  4.401e-03   335.097  < 2e-16 ***
ORIGIN_SZYSSZ01      -1.552e-01  5.643e-03   -27.496  < 2e-16 ***
ORIGIN_SZYSSZ02       8.958e-01  4.973e-03   180.144  < 2e-16 ***
ORIGIN_SZYSSZ03       1.757e+00  4.275e-03   411.050  < 2e-16 ***
ORIGIN_SZYSSZ04       8.439e-01  4.538e-03   185.955  < 2e-16 ***
ORIGIN_SZYSSZ05      -9.995e-02  5.920e-03   -16.884  < 2e-16 ***
ORIGIN_SZYSSZ06      -1.175e+00  1.079e-02  -108.835  < 2e-16 ***
ORIGIN_SZYSSZ07      -1.202e+00  1.127e-02  -106.642  < 2e-16 ***
ORIGIN_SZYSSZ08       1.244e-02  6.104e-03     2.039  0.04148 *  
ORIGIN_SZYSSZ09       1.385e+00  4.239e-03   326.757  < 2e-16 ***
log(DESTIN_AGE25_64)  2.298e-02  8.832e-05   260.146  < 2e-16 ***
log(dist)            -6.947e-01  1.295e-04 -5363.438  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 60796037  on 14733  degrees of freedom
Residual deviance: 26726668  on 14453  degrees of freedom
AIC: 26818857

Number of Fisher Scoring iterations: 7

We can examine how the constraints hold for destinations this time.

Code

CalcRSquared(orcSIM$data$TRIPS, orcSIM$fitted.values)

[1] 0.4165837

6.7 Destination constrained

In this section, we will fit a destination constrained SIM by using the code chunk below.

Code

decSIM <- glm(formula = TRIPS ~ 
                DESTIN_SZ + 
                log(ORIGIN_AGE25_64) + 
                log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
summary(decSIM)

Call:
glm(formula = TRIPS ~ DESTIN_SZ + log(ORIGIN_AGE25_64) + log(dist), 
    family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)

Coefficients:
                       Estimate Std. Error   z value Pr(>|z|)    
(Intercept)          10.8110189  0.0033476  3229.499  < 2e-16 ***
DESTIN_SZAMSZ02       0.1775885  0.0041530    42.761  < 2e-16 ***
DESTIN_SZAMSZ03       0.2064091  0.0040888    50.482  < 2e-16 ***
DESTIN_SZAMSZ04      -0.9406455  0.0060637  -155.127  < 2e-16 ***
DESTIN_SZAMSZ05      -1.1578100  0.0061804  -187.337  < 2e-16 ***
DESTIN_SZAMSZ06      -0.8861493  0.0059241  -149.584  < 2e-16 ***
DESTIN_SZAMSZ07      -1.7712447  0.0096070  -184.370  < 2e-16 ***
DESTIN_SZAMSZ08      -1.0707197  0.0067763  -158.009  < 2e-16 ***
DESTIN_SZAMSZ09      -0.9682250  0.0060435  -160.210  < 2e-16 ***
DESTIN_SZAMSZ10       0.2612773  0.0043738    59.737  < 2e-16 ***
DESTIN_SZAMSZ11      -0.3714704  0.0086200   -43.094  < 2e-16 ***
DESTIN_SZAMSZ12       0.0250455  0.0049850     5.024 5.06e-07 ***
DESTIN_SZBDSZ01       0.5154763  0.0037827   136.271  < 2e-16 ***
DESTIN_SZBDSZ02      -0.2843120  0.0049517   -57.417  < 2e-16 ***
DESTIN_SZBDSZ03      -0.0134646  0.0042692    -3.154  0.00161 ** 
DESTIN_SZBDSZ04       1.0014441  0.0034463   290.582  < 2e-16 ***
DESTIN_SZBDSZ05       0.3721573  0.0038992    95.445  < 2e-16 ***
DESTIN_SZBDSZ06       0.2013935  0.0042182    47.744  < 2e-16 ***
DESTIN_SZBDSZ07      -1.0642612  0.0092942  -114.508  < 2e-16 ***
DESTIN_SZBDSZ08      -1.7769370  0.0105721  -168.077  < 2e-16 ***
DESTIN_SZBKSZ01      -1.1944766  0.0065580  -182.141  < 2e-16 ***
DESTIN_SZBKSZ02      -0.2604946  0.0052044   -50.053  < 2e-16 ***
DESTIN_SZBKSZ03      -0.5905775  0.0055618  -106.184  < 2e-16 ***
DESTIN_SZBKSZ04      -0.0521573  0.0048274   -10.804  < 2e-16 ***
DESTIN_SZBKSZ05      -0.8258599  0.0057094  -144.650  < 2e-16 ***
DESTIN_SZBKSZ06      -0.8696763  0.0060934  -142.725  < 2e-16 ***
DESTIN_SZBKSZ07       0.2216292  0.0040334    54.949  < 2e-16 ***
DESTIN_SZBKSZ08      -1.1179375  0.0068749  -162.612  < 2e-16 ***
DESTIN_SZBKSZ09      -0.2888733  0.0049056   -58.886  < 2e-16 ***
DESTIN_SZBLSZ01      -0.4487061  0.0070226   -63.894  < 2e-16 ***
DESTIN_SZBLSZ02       0.6343096  0.0065174    97.326  < 2e-16 ***
DESTIN_SZBLSZ03       1.3492337  0.0074135   181.997  < 2e-16 ***
DESTIN_SZBLSZ04      -0.0339193  0.0131568    -2.578  0.00993 ** 
DESTIN_SZBMSZ01      -0.3497912  0.0046910   -74.567  < 2e-16 ***
DESTIN_SZBMSZ02      -0.5995634  0.0048828  -122.792  < 2e-16 ***
DESTIN_SZBMSZ03      -0.8726401  0.0056851  -153.495  < 2e-16 ***
DESTIN_SZBMSZ04      -0.5350402  0.0048888  -109.442  < 2e-16 ***
DESTIN_SZBMSZ05      -0.4981814  0.0065971   -75.515  < 2e-16 ***
DESTIN_SZBMSZ06      -2.0640198  0.0123050  -167.739  < 2e-16 ***
DESTIN_SZBMSZ07      -0.3100988  0.0045283   -68.480  < 2e-16 ***
DESTIN_SZBMSZ08      -1.2748152  0.0062622  -203.573  < 2e-16 ***
DESTIN_SZBMSZ09      -2.8056325  0.0143532  -195.471  < 2e-16 ***
DESTIN_SZBMSZ10      -1.9166407  0.0089273  -214.693  < 2e-16 ***
DESTIN_SZBMSZ11      -1.7261160  0.0079281  -217.722  < 2e-16 ***
DESTIN_SZBMSZ12      -1.1495908  0.0077721  -147.912  < 2e-16 ***
DESTIN_SZBMSZ13      -0.5428008  0.0050824  -106.799  < 2e-16 ***
DESTIN_SZBMSZ14      -1.1422302  0.0076325  -149.653  < 2e-16 ***
DESTIN_SZBMSZ15      -1.2217517  0.0068685  -177.878  < 2e-16 ***
DESTIN_SZBMSZ16      -2.4074288  0.0107900  -223.116  < 2e-16 ***
DESTIN_SZBMSZ17      -2.6985491  0.0164771  -163.776  < 2e-16 ***
DESTIN_SZBPSZ01      -0.6183085  0.0054605  -113.233  < 2e-16 ***
DESTIN_SZBPSZ02      -1.4579175  0.0083271  -175.080  < 2e-16 ***
DESTIN_SZBPSZ03      -1.0775392  0.0075109  -143.463  < 2e-16 ***
DESTIN_SZBPSZ04      -0.6645303  0.0058070  -114.436  < 2e-16 ***
DESTIN_SZBPSZ05       0.3449386  0.0039504    87.318  < 2e-16 ***
DESTIN_SZBPSZ06      -0.9360064  0.0077394  -120.941  < 2e-16 ***
DESTIN_SZBPSZ07      -0.6850065  0.0077761   -88.091  < 2e-16 ***
DESTIN_SZBSSZ01      -0.3144210  0.0045803   -68.647  < 2e-16 ***
DESTIN_SZBSSZ02      -0.7531935  0.0051075  -147.469  < 2e-16 ***
DESTIN_SZBSSZ03       0.1964072  0.0038255    51.342  < 2e-16 ***
DESTIN_SZBTSZ01       0.0749897  0.0041584    18.033  < 2e-16 ***
DESTIN_SZBTSZ02      -0.8214254  0.0065659  -125.105  < 2e-16 ***
DESTIN_SZBTSZ03      -0.1672596  0.0047942   -34.888  < 2e-16 ***
DESTIN_SZBTSZ04      -1.7727273  0.0103706  -170.938  < 2e-16 ***
DESTIN_SZBTSZ05      -0.8162630  0.0067401  -121.105  < 2e-16 ***
DESTIN_SZBTSZ06      -0.8159130  0.0059754  -136.546  < 2e-16 ***
DESTIN_SZBTSZ07      -2.1139258  0.0105602  -200.178  < 2e-16 ***
DESTIN_SZBTSZ08      -1.3565179  0.0086828  -156.231  < 2e-16 ***
DESTIN_SZCBSZ01      -4.6643129  0.3162417   -14.749  < 2e-16 ***
DESTIN_SZCCSZ01      -1.0088833  0.0080155  -125.866  < 2e-16 ***
DESTIN_SZCHSZ01      -1.1909317  0.0095262  -125.017  < 2e-16 ***
DESTIN_SZCHSZ02       0.0890035  0.0052277    17.025  < 2e-16 ***
DESTIN_SZCHSZ03       1.4883985  0.0039094   380.724  < 2e-16 ***
DESTIN_SZCKSZ01      -0.1684738  0.0047561   -35.422  < 2e-16 ***
DESTIN_SZCKSZ02      -0.4314614  0.0051537   -83.720  < 2e-16 ***
DESTIN_SZCKSZ03       0.6413457  0.0038639   165.983  < 2e-16 ***
DESTIN_SZCKSZ04      -0.6370791  0.0059869  -106.412  < 2e-16 ***
DESTIN_SZCKSZ05      -0.4185112  0.0065348   -64.044  < 2e-16 ***
DESTIN_SZCKSZ06       0.7003888  0.0045139   155.163  < 2e-16 ***
DESTIN_SZCLSZ01       0.3751343  0.0047400    79.143  < 2e-16 ***
DESTIN_SZCLSZ02      -2.2913668  0.0133371  -171.804  < 2e-16 ***
DESTIN_SZCLSZ03      -1.0498490  0.0076548  -137.149  < 2e-16 ***
DESTIN_SZCLSZ04      -0.1118915  0.0044886   -24.928  < 2e-16 ***
DESTIN_SZCLSZ05      -1.3113032  0.0084067  -155.983  < 2e-16 ***
DESTIN_SZCLSZ06       0.1661786  0.0040203    41.334  < 2e-16 ***
DESTIN_SZCLSZ07      -0.6429895  0.0052617  -122.202  < 2e-16 ***
DESTIN_SZCLSZ08      -0.4271702  0.0057208   -74.670  < 2e-16 ***
DESTIN_SZCLSZ09       0.3882136  0.0063758    60.888  < 2e-16 ***
DESTIN_SZDTSZ02      -3.0106480  0.0348374   -86.420  < 2e-16 ***
DESTIN_SZDTSZ03      -1.4195712  0.0144110   -98.506  < 2e-16 ***
DESTIN_SZDTSZ13      -2.2368573  0.0161427  -138.567  < 2e-16 ***
DESTIN_SZGLSZ01       0.0013721  0.0051224     0.268  0.78881    
DESTIN_SZGLSZ02      -0.3376674  0.0046195   -73.097  < 2e-16 ***
DESTIN_SZGLSZ03       0.3659900  0.0038384    95.350  < 2e-16 ***
DESTIN_SZGLSZ04       0.2969928  0.0038026    78.103  < 2e-16 ***
DESTIN_SZGLSZ05       0.1786445  0.0038853    45.980  < 2e-16 ***
DESTIN_SZHGSZ01       0.2979206  0.0038825    76.735  < 2e-16 ***
DESTIN_SZHGSZ02      -0.5701034  0.0051182  -111.388  < 2e-16 ***
DESTIN_SZHGSZ03      -1.0387610  0.0061020  -170.233  < 2e-16 ***
DESTIN_SZHGSZ04      -0.2264881  0.0043617   -51.926  < 2e-16 ***
DESTIN_SZHGSZ05      -0.2287090  0.0044851   -50.993  < 2e-16 ***
DESTIN_SZHGSZ06      -0.7896437  0.0054081  -146.010  < 2e-16 ***
DESTIN_SZHGSZ07       0.2268880  0.0040336    56.249  < 2e-16 ***
DESTIN_SZHGSZ08      -0.4260784  0.0048967   -87.013  < 2e-16 ***
DESTIN_SZHGSZ09       0.1027784  0.0051341    20.019  < 2e-16 ***
DESTIN_SZHGSZ10      -2.8571803  0.0262064  -109.026  < 2e-16 ***
DESTIN_SZJESZ01      -0.0843635  0.0048222   -17.495  < 2e-16 ***
DESTIN_SZJESZ02      -0.5197682  0.0051511  -100.904  < 2e-16 ***
DESTIN_SZJESZ03      -0.6250311  0.0056619  -110.392  < 2e-16 ***
DESTIN_SZJESZ04      -0.3937360  0.0065536   -60.080  < 2e-16 ***
DESTIN_SZJESZ05      -0.9748291  0.0097665   -99.814  < 2e-16 ***
DESTIN_SZJESZ06       0.3642736  0.0040600    89.722  < 2e-16 ***
DESTIN_SZJESZ07      -1.1571882  0.0081557  -141.887  < 2e-16 ***
DESTIN_SZJESZ08      -0.5955747  0.0078071   -76.286  < 2e-16 ***
DESTIN_SZJESZ09      -0.3629500  0.0053966   -67.256  < 2e-16 ***
DESTIN_SZJESZ10       0.7691552  0.0069348   110.912  < 2e-16 ***
DESTIN_SZJESZ11       0.9365743  0.0065801   142.335  < 2e-16 ***
DESTIN_SZJWSZ01      -0.4568805  0.0064536   -70.795  < 2e-16 ***
DESTIN_SZJWSZ02      -0.2880426  0.0051632   -55.788  < 2e-16 ***
DESTIN_SZJWSZ03       0.6680404  0.0039264   170.142  < 2e-16 ***
DESTIN_SZJWSZ04       0.9492158  0.0037186   255.262  < 2e-16 ***
DESTIN_SZJWSZ05      -0.1938053  0.0060810   -31.871  < 2e-16 ***
DESTIN_SZJWSZ06       0.3813164  0.0054551    69.900  < 2e-16 ***
DESTIN_SZJWSZ07      -1.2676010  0.0280038   -45.265  < 2e-16 ***
DESTIN_SZJWSZ08       0.5013149  0.0044573   112.471  < 2e-16 ***
DESTIN_SZJWSZ09       1.4161404  0.0033937   417.291  < 2e-16 ***
DESTIN_SZKLSZ01      -0.6909444  0.0051540  -134.059  < 2e-16 ***
DESTIN_SZKLSZ02      -0.8146023  0.0057129  -142.589  < 2e-16 ***
DESTIN_SZKLSZ03      -1.3956114  0.0065167  -214.161  < 2e-16 ***
DESTIN_SZKLSZ04      -1.9070281  0.0087370  -218.270  < 2e-16 ***
DESTIN_SZKLSZ05      -0.9293576  0.0071070  -130.766  < 2e-16 ***
DESTIN_SZKLSZ06      -2.5402234  0.0362062   -70.160  < 2e-16 ***
DESTIN_SZKLSZ07      -1.2017213  0.0065751  -182.769  < 2e-16 ***
DESTIN_SZKLSZ08      -0.6083433  0.0050916  -119.480  < 2e-16 ***
DESTIN_SZLKSZ01      -1.5186810  0.0204155   -74.389  < 2e-16 ***
DESTIN_SZMDSZ01      -1.4601772  0.0198347   -73.617  < 2e-16 ***
DESTIN_SZMDSZ02      -1.1554609  0.0111345  -103.773  < 2e-16 ***
DESTIN_SZMDSZ03      -2.9919337  0.0250838  -119.277  < 2e-16 ***
DESTIN_SZMPSZ01      -1.1705809  0.0077128  -151.771  < 2e-16 ***
DESTIN_SZMPSZ02      -0.9380957  0.0060321  -155.517  < 2e-16 ***
DESTIN_SZMPSZ03      -0.1761013  0.0046389   -37.962  < 2e-16 ***
DESTIN_SZMUSZ02      -2.4525115  0.0199630  -122.853  < 2e-16 ***
DESTIN_SZNTSZ01      -3.6605524  0.0447752   -81.754  < 2e-16 ***
DESTIN_SZNTSZ02      -2.0082021  0.0108736  -184.686  < 2e-16 ***
DESTIN_SZNTSZ03      -1.2387489  0.0076141  -162.691  < 2e-16 ***
DESTIN_SZNTSZ05      -1.8054361  0.0249540   -72.351  < 2e-16 ***
DESTIN_SZNTSZ06      -2.9500517  0.0428601   -68.830  < 2e-16 ***
DESTIN_SZNVSZ01      -0.4089022  0.0044288   -92.327  < 2e-16 ***
DESTIN_SZNVSZ02      -0.6865452  0.0052770  -130.102  < 2e-16 ***
DESTIN_SZNVSZ03      -0.7333670  0.0054243  -135.199  < 2e-16 ***
DESTIN_SZNVSZ04      -2.2095097  0.0106997  -206.503  < 2e-16 ***
DESTIN_SZNVSZ05      -1.8721104  0.0089058  -210.212  < 2e-16 ***
DESTIN_SZPGSZ01      -1.8756618  0.0153008  -122.586  < 2e-16 ***
DESTIN_SZPGSZ02      -0.9435337  0.0067224  -140.356  < 2e-16 ***
DESTIN_SZPGSZ03       0.3458476  0.0040152    86.134  < 2e-16 ***
DESTIN_SZPGSZ04      -0.0271485  0.0044805    -6.059 1.37e-09 ***
DESTIN_SZPGSZ05      -0.8920273  0.0070730  -126.117  < 2e-16 ***
DESTIN_SZPLSZ01      -0.2153087  0.0068270   -31.538  < 2e-16 ***
DESTIN_SZPLSZ02      -1.3646116  0.0131155  -104.046  < 2e-16 ***
DESTIN_SZPLSZ03      -0.0869245  0.0095838    -9.070  < 2e-16 ***
DESTIN_SZPLSZ04      -0.2574560  0.0093336   -27.584  < 2e-16 ***
DESTIN_SZPLSZ05      -0.7186364  0.0116835   -61.509  < 2e-16 ***
DESTIN_SZPNSZ01       1.1326963  0.0049977   226.643  < 2e-16 ***
DESTIN_SZPNSZ02       1.6516855  0.0064492   256.106  < 2e-16 ***
DESTIN_SZPNSZ03       0.8504093  0.0077034   110.394  < 2e-16 ***
DESTIN_SZPNSZ04       1.6891381  0.0075802   222.836  < 2e-16 ***
DESTIN_SZPNSZ05       0.7402750  0.0115948    63.845  < 2e-16 ***
DESTIN_SZPRSZ01      -1.0257636  0.0084652  -121.175  < 2e-16 ***
DESTIN_SZPRSZ02      -0.2028503  0.0049839   -40.701  < 2e-16 ***
DESTIN_SZPRSZ03       0.5560483  0.0038496   144.442  < 2e-16 ***
DESTIN_SZPRSZ04      -0.6824142  0.0079047   -86.330  < 2e-16 ***
DESTIN_SZPRSZ05       0.0316117  0.0044946     7.033 2.02e-12 ***
DESTIN_SZPRSZ06       0.3706283  0.0052006    71.267  < 2e-16 ***
DESTIN_SZPRSZ07      -1.4740460  0.0117304  -125.661  < 2e-16 ***
DESTIN_SZPRSZ08      -0.7869180  0.0064862  -121.321  < 2e-16 ***
DESTIN_SZQTSZ01      -1.2790095  0.0085392  -149.781  < 2e-16 ***
DESTIN_SZQTSZ02      -1.4989188  0.0073423  -204.149  < 2e-16 ***
DESTIN_SZQTSZ03      -0.9334132  0.0064035  -145.765  < 2e-16 ***
DESTIN_SZQTSZ04      -1.0506142  0.0065335  -160.805  < 2e-16 ***
DESTIN_SZQTSZ05      -0.9765013  0.0058471  -167.006  < 2e-16 ***
DESTIN_SZQTSZ06      -1.2206088  0.0063560  -192.042  < 2e-16 ***
DESTIN_SZQTSZ07      -1.6794007  0.0108727  -154.460  < 2e-16 ***
DESTIN_SZQTSZ08      -0.1214413  0.0047980   -25.311  < 2e-16 ***
DESTIN_SZQTSZ09      -0.5252607  0.0057371   -91.555  < 2e-16 ***
DESTIN_SZQTSZ10      -0.5981644  0.0054192  -110.378  < 2e-16 ***
DESTIN_SZQTSZ11      -0.0766021  0.0053446   -14.333  < 2e-16 ***
DESTIN_SZQTSZ12      -0.6153017  0.0070680   -87.054  < 2e-16 ***
DESTIN_SZQTSZ13      -0.1690535  0.0051315   -32.944  < 2e-16 ***
DESTIN_SZQTSZ14      -0.5398362  0.0062233   -86.744  < 2e-16 ***
DESTIN_SZQTSZ15      -0.1873015  0.0073132   -25.611  < 2e-16 ***
DESTIN_SZRCSZ01      -0.5875494  0.0071798   -81.833  < 2e-16 ***
DESTIN_SZRCSZ06      -2.0856090  0.0188789  -110.473  < 2e-16 ***
DESTIN_SZRVSZ01      -2.6183708  0.0162319  -161.310  < 2e-16 ***
DESTIN_SZRVSZ02      -3.1882190  0.0326141   -97.756  < 2e-16 ***
DESTIN_SZRVSZ03      -2.5981974  0.0135074  -192.353  < 2e-16 ***
DESTIN_SZRVSZ04      -1.9741504  0.0154961  -127.396  < 2e-16 ***
DESTIN_SZRVSZ05      -3.1547734  0.0256310  -123.084  < 2e-16 ***
DESTIN_SZSBSZ01      -0.3097949  0.0060601   -51.121  < 2e-16 ***
DESTIN_SZSBSZ02      -1.1229132  0.0076338  -147.097  < 2e-16 ***
DESTIN_SZSBSZ03       0.6289715  0.0041400   151.926  < 2e-16 ***
DESTIN_SZSBSZ04       0.1419430  0.0051357    27.638  < 2e-16 ***
DESTIN_SZSBSZ05      -0.9256413  0.0071963  -128.628  < 2e-16 ***
DESTIN_SZSBSZ06      -2.3487368  0.0221611  -105.984  < 2e-16 ***
DESTIN_SZSBSZ07      -0.7864630  0.0181706   -43.282  < 2e-16 ***
DESTIN_SZSBSZ08       1.3240051  0.0051598   256.599  < 2e-16 ***
DESTIN_SZSBSZ09       0.8431156  0.0048330   174.449  < 2e-16 ***
DESTIN_SZSESZ02      -0.2385874  0.0046618   -51.180  < 2e-16 ***
DESTIN_SZSESZ03       0.5439188  0.0036932   147.276  < 2e-16 ***
DESTIN_SZSESZ04      -0.6715716  0.0054222  -123.856  < 2e-16 ***
DESTIN_SZSESZ05      -0.3601932  0.0047508   -75.818  < 2e-16 ***
DESTIN_SZSESZ06      -0.6088413  0.0057017  -106.782  < 2e-16 ***
DESTIN_SZSESZ07      -2.9477507  0.0226797  -129.973  < 2e-16 ***
DESTIN_SZSGSZ01      -0.5100640  0.0058280   -87.519  < 2e-16 ***
DESTIN_SZSGSZ02      -0.0439941  0.0051633    -8.520  < 2e-16 ***
DESTIN_SZSGSZ03      -0.3700648  0.0047152   -78.483  < 2e-16 ***
DESTIN_SZSGSZ04      -0.3021335  0.0046865   -64.468  < 2e-16 ***
DESTIN_SZSGSZ05      -2.2253287  0.0097908  -227.288  < 2e-16 ***
DESTIN_SZSGSZ06       0.2963602  0.0037948    78.097  < 2e-16 ***
DESTIN_SZSGSZ07      -0.5940373  0.0051371  -115.637  < 2e-16 ***
DESTIN_SZSISZ01      -1.4528976  0.0257790   -56.360  < 2e-16 ***
DESTIN_SZSKSZ01      -0.0374952  0.0066885    -5.606 2.07e-08 ***
DESTIN_SZSKSZ02       0.7271418  0.0050281   144.617  < 2e-16 ***
DESTIN_SZSKSZ03      -0.0640794  0.0059146   -10.834  < 2e-16 ***
DESTIN_SZSKSZ04      -0.5610767  0.0139676   -40.170  < 2e-16 ***
DESTIN_SZSKSZ05       0.1510974  0.0104871    14.408  < 2e-16 ***
DESTIN_SZSLSZ01      -0.5823031  0.0083356   -69.858  < 2e-16 ***
DESTIN_SZSLSZ04      -0.8166665  0.0070329  -116.122  < 2e-16 ***
DESTIN_SZSRSZ01      -2.3241796  0.0127215  -182.696  < 2e-16 ***
DESTIN_SZTHSZ01      -2.8157635  0.0366840   -76.757  < 2e-16 ***
DESTIN_SZTHSZ03      -2.1005978  0.0250842   -83.742  < 2e-16 ***
DESTIN_SZTHSZ04      -2.1246250  0.0213690   -99.425  < 2e-16 ***
DESTIN_SZTHSZ06      -1.4571092  0.0150031   -97.121  < 2e-16 ***
DESTIN_SZTMSZ01      -0.1234559  0.0055152   -22.385  < 2e-16 ***
DESTIN_SZTMSZ02       1.5961628  0.0032599   489.635  < 2e-16 ***
DESTIN_SZTMSZ03       0.6977233  0.0037138   187.875  < 2e-16 ***
DESTIN_SZTMSZ04       0.8606606  0.0037592   228.947  < 2e-16 ***
DESTIN_SZTMSZ05       0.3750655  0.0051281    73.140  < 2e-16 ***
DESTIN_SZTNSZ01      -1.2624562  0.0066979  -188.485  < 2e-16 ***
DESTIN_SZTNSZ02      -2.0761581  0.0096538  -215.062  < 2e-16 ***
DESTIN_SZTNSZ03      -2.1128125  0.0115717  -182.584  < 2e-16 ***
DESTIN_SZTNSZ04      -1.2417494  0.0068502  -181.271  < 2e-16 ***
DESTIN_SZTPSZ01      -0.7094356  0.0055768  -127.211  < 2e-16 ***
DESTIN_SZTPSZ02       0.1491604  0.0037260    40.032  < 2e-16 ***
DESTIN_SZTPSZ03      -0.4973355  0.0054878   -90.626  < 2e-16 ***
DESTIN_SZTPSZ04      -1.5160395  0.0071592  -211.761  < 2e-16 ***
DESTIN_SZTPSZ05      -0.9196565  0.0056750  -162.054  < 2e-16 ***
DESTIN_SZTPSZ06      -0.2710649  0.0062637   -43.276  < 2e-16 ***
DESTIN_SZTPSZ07      -2.0198681  0.0116556  -173.296  < 2e-16 ***
DESTIN_SZTPSZ08      -1.4881412  0.0085532  -173.987  < 2e-16 ***
DESTIN_SZTPSZ09      -0.5901273  0.0059394   -99.358  < 2e-16 ***
DESTIN_SZTPSZ10      -1.1215711  0.0084488  -132.749  < 2e-16 ***
DESTIN_SZTPSZ11      -0.4837089  0.0050905   -95.022  < 2e-16 ***
DESTIN_SZTPSZ12      -0.8653927  0.0061326  -141.113  < 2e-16 ***
DESTIN_SZTSSZ01      -0.5515103  0.0208541   -26.446  < 2e-16 ***
DESTIN_SZTSSZ02       0.8373778  0.0093757    89.314  < 2e-16 ***
DESTIN_SZTSSZ03       1.7021888  0.0064394   264.340  < 2e-16 ***
DESTIN_SZTSSZ04       1.5355016  0.0067855   226.292  < 2e-16 ***
DESTIN_SZTSSZ05       1.6932319  0.0073725   229.668  < 2e-16 ***
DESTIN_SZTSSZ06       0.4567808  0.0137927    33.118  < 2e-16 ***
DESTIN_SZWCSZ01       1.3967640  0.0045392   307.711  < 2e-16 ***
DESTIN_SZWCSZ02      -0.4560229  0.0122949   -37.090  < 2e-16 ***
DESTIN_SZWCSZ03      -2.0710051  0.0325121   -63.699  < 2e-16 ***
DESTIN_SZWDSZ01       1.5137342  0.0034774   435.310  < 2e-16 ***
DESTIN_SZWDSZ02      -0.3005475  0.0055149   -54.497  < 2e-16 ***
DESTIN_SZWDSZ03       1.2514543  0.0036112   346.550  < 2e-16 ***
DESTIN_SZWDSZ04      -0.1702528  0.0058295   -29.205  < 2e-16 ***
DESTIN_SZWDSZ05      -0.0005419  0.0053911    -0.101  0.91994    
DESTIN_SZWDSZ06       0.5203361  0.0040318   129.058  < 2e-16 ***
DESTIN_SZWDSZ07       0.6006472  0.0061745    97.279  < 2e-16 ***
DESTIN_SZWDSZ08       0.6650867  0.0060867   109.268  < 2e-16 ***
DESTIN_SZWDSZ09       0.6237312  0.0044830   139.132  < 2e-16 ***
DESTIN_SZYSSZ01       1.0471638  0.0038255   273.732  < 2e-16 ***
DESTIN_SZYSSZ02       0.2341114  0.0048213    48.558  < 2e-16 ***
DESTIN_SZYSSZ03      -0.0916446  0.0051335   -17.852  < 2e-16 ***
DESTIN_SZYSSZ04      -0.0085536  0.0048684    -1.757  0.07892 .  
DESTIN_SZYSSZ05      -1.5775071  0.0100297  -157.283  < 2e-16 ***
DESTIN_SZYSSZ06      -1.8130307  0.0098617  -183.846  < 2e-16 ***
DESTIN_SZYSSZ07      -1.1703963  0.0111525  -104.945  < 2e-16 ***
DESTIN_SZYSSZ08       0.5253514  0.0039556   132.813  < 2e-16 ***
DESTIN_SZYSSZ09       0.4353435  0.0038890   111.943  < 2e-16 ***
log(ORIGIN_AGE25_64)  0.2249135  0.0001404  1602.353  < 2e-16 ***
log(dist)            -0.6989356  0.0001287 -5431.279  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 60796037  on 14733  degrees of freedom
Residual deviance: 26208384  on 14452  degrees of freedom
AIC: 26300575

Number of Fisher Scoring iterations: 7

We can examine how the constraints hold for destinations this time.

Code

CalcRSquared(decSIM$data$TRIPS, decSIM$fitted.values)

[1] 0.4972985

6.8 Doubly constrained

In this section, we will fit a doubly constrained SIM by using the code chunk below.

The general formula of Doubly Constrained Spatial Interaction Model

Code

dbcSIM <- glm(formula = TRIPS ~ 
                ORIGIN_SZ + 
                DESTIN_SZ + 
                log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
summary(dbcSIM)

Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(dist), family = poisson(link = "log"), 
    data = SIM_data, na.action = na.exclude)

Coefficients:
                  Estimate Std. Error   z value Pr(>|z|)    
(Intercept)     12.4165310  0.0043949  2825.242  < 2e-16 ***
ORIGIN_SZAMSZ02  0.9496891  0.0045740   207.630  < 2e-16 ***
ORIGIN_SZAMSZ03  0.5519174  0.0046672   118.253  < 2e-16 ***
ORIGIN_SZAMSZ04  0.1028140  0.0052468    19.596  < 2e-16 ***
ORIGIN_SZAMSZ05  0.0822549  0.0058663    14.022  < 2e-16 ***
ORIGIN_SZAMSZ06  0.6617809  0.0052580   125.861  < 2e-16 ***
ORIGIN_SZAMSZ07 -0.9508298  0.0097681   -97.340  < 2e-16 ***
ORIGIN_SZAMSZ08 -0.7271779  0.0090946   -79.958  < 2e-16 ***
ORIGIN_SZAMSZ09  0.4896781  0.0055203    88.704  < 2e-16 ***
ORIGIN_SZAMSZ10  0.4819428  0.0048175   100.040  < 2e-16 ***
ORIGIN_SZAMSZ11 -1.7719841  0.0130695  -135.582  < 2e-16 ***
ORIGIN_SZAMSZ12 -1.7679107  0.0108777  -162.526  < 2e-16 ***
ORIGIN_SZBDSZ01  0.8314812  0.0045187   184.010  < 2e-16 ***
ORIGIN_SZBDSZ02  0.4305836  0.0052535    81.961  < 2e-16 ***
ORIGIN_SZBDSZ03  0.8009370  0.0046384   172.676  < 2e-16 ***
ORIGIN_SZBDSZ04  1.4562985  0.0040456   359.971  < 2e-16 ***
ORIGIN_SZBDSZ05  0.4501939  0.0046960    95.867  < 2e-16 ***
ORIGIN_SZBDSZ06  0.7745026  0.0047424   163.314  < 2e-16 ***
ORIGIN_SZBDSZ07 -1.1784123  0.0098105  -120.117  < 2e-16 ***
ORIGIN_SZBDSZ08 -0.9830996  0.0091135  -107.873  < 2e-16 ***
ORIGIN_SZBKSZ01 -0.3042966  0.0067086   -45.359  < 2e-16 ***
ORIGIN_SZBKSZ02  0.4801541  0.0054160    88.655  < 2e-16 ***
ORIGIN_SZBKSZ03  0.7823931  0.0052007   150.440  < 2e-16 ***
ORIGIN_SZBKSZ04 -0.1292545  0.0061735   -20.937  < 2e-16 ***
ORIGIN_SZBKSZ05 -0.0258584  0.0060192    -4.296 1.74e-05 ***
ORIGIN_SZBKSZ06  0.1994719  0.0061206    32.590  < 2e-16 ***
ORIGIN_SZBKSZ07  0.7434860  0.0046598   159.553  < 2e-16 ***
ORIGIN_SZBKSZ08  0.1625007  0.0055219    29.428  < 2e-16 ***
ORIGIN_SZBKSZ09 -0.0864293  0.0059533   -14.518  < 2e-16 ***
ORIGIN_SZBLSZ01 -2.1022485  0.0150316  -139.855  < 2e-16 ***
ORIGIN_SZBLSZ02 -2.9460181  0.0195760  -150.491  < 2e-16 ***
ORIGIN_SZBLSZ03 -4.9412872  0.0398540  -123.985  < 2e-16 ***
ORIGIN_SZBLSZ04 -2.8143593  0.0239209  -117.653  < 2e-16 ***
ORIGIN_SZBMSZ01 -0.0264561  0.0053639    -4.932 8.13e-07 ***
ORIGIN_SZBMSZ02 -0.8656513  0.0068511  -126.353  < 2e-16 ***
ORIGIN_SZBMSZ03 -0.1723467  0.0059613   -28.911  < 2e-16 ***
ORIGIN_SZBMSZ04  0.2169844  0.0053578    40.499  < 2e-16 ***
ORIGIN_SZBMSZ05 -2.0252956  0.0126107  -160.602  < 2e-16 ***
ORIGIN_SZBMSZ06 -1.7642018  0.0163931  -107.619  < 2e-16 ***
ORIGIN_SZBMSZ07 -0.3271629  0.0058137   -56.274  < 2e-16 ***
ORIGIN_SZBMSZ08 -0.2533255  0.0059335   -42.694  < 2e-16 ***
ORIGIN_SZBMSZ09 -0.7712635  0.0087939   -87.704  < 2e-16 ***
ORIGIN_SZBMSZ10 -1.0098048  0.0092519  -109.145  < 2e-16 ***
ORIGIN_SZBMSZ11 -0.3816187  0.0067302   -56.702  < 2e-16 ***
ORIGIN_SZBMSZ12 -0.6666616  0.0095680   -69.676  < 2e-16 ***
ORIGIN_SZBMSZ13 -0.0076108  0.0059040    -1.289  0.19737    
ORIGIN_SZBMSZ14 -0.1682476  0.0069391   -24.246  < 2e-16 ***
ORIGIN_SZBMSZ15  0.0904585  0.0062822    14.399  < 2e-16 ***
ORIGIN_SZBMSZ16 -1.1808741  0.0092258  -127.997  < 2e-16 ***
ORIGIN_SZBMSZ17 -1.7189127  0.0158408  -108.512  < 2e-16 ***
ORIGIN_SZBPSZ01  0.4294645  0.0058051    73.980  < 2e-16 ***
ORIGIN_SZBPSZ02  0.5028906  0.0068169    73.771  < 2e-16 ***
ORIGIN_SZBPSZ03  0.6656178  0.0066126   100.658  < 2e-16 ***
ORIGIN_SZBPSZ04  0.5203612  0.0053224    97.769  < 2e-16 ***
ORIGIN_SZBPSZ05  0.5377769  0.0047907   112.256  < 2e-16 ***
ORIGIN_SZBPSZ06 -1.2327809  0.0094950  -129.835  < 2e-16 ***
ORIGIN_SZBPSZ07 -0.9035255  0.0088739  -101.818  < 2e-16 ***
ORIGIN_SZBSSZ01  0.1210027  0.0053990    22.412  < 2e-16 ***
ORIGIN_SZBSSZ02  0.4618449  0.0048641    94.951  < 2e-16 ***
ORIGIN_SZBSSZ03  0.2160739  0.0047835    45.170  < 2e-16 ***
ORIGIN_SZBTSZ01 -0.1108042  0.0055599   -19.929  < 2e-16 ***
ORIGIN_SZBTSZ02 -0.8911221  0.0079213  -112.498  < 2e-16 ***
ORIGIN_SZBTSZ03 -0.2203980  0.0059325   -37.151  < 2e-16 ***
ORIGIN_SZBTSZ04 -0.6427946  0.0105438   -60.964  < 2e-16 ***
ORIGIN_SZBTSZ05 -1.4662312  0.0111784  -131.166  < 2e-16 ***
ORIGIN_SZBTSZ06 -0.6105884  0.0073456   -83.123  < 2e-16 ***
ORIGIN_SZBTSZ07 -1.9041317  0.0132781  -143.404  < 2e-16 ***
ORIGIN_SZBTSZ08 -1.0627939  0.0095982  -110.728  < 2e-16 ***
ORIGIN_SZCBSZ01 -2.9365941  0.0548632   -53.526  < 2e-16 ***
ORIGIN_SZCCSZ01 -1.5313555  0.0134599  -113.772  < 2e-16 ***
ORIGIN_SZCHSZ01 -1.2034494  0.0119468  -100.734  < 2e-16 ***
ORIGIN_SZCHSZ02 -0.8299415  0.0081984  -101.232  < 2e-16 ***
ORIGIN_SZCHSZ03 -0.5143946  0.0061944   -83.042  < 2e-16 ***
ORIGIN_SZCKSZ01  0.2372583  0.0053612    44.255  < 2e-16 ***
ORIGIN_SZCKSZ02  0.9124836  0.0054472   167.515  < 2e-16 ***
ORIGIN_SZCKSZ03  0.7237808  0.0048401   149.539  < 2e-16 ***
ORIGIN_SZCKSZ04  1.6884022  0.0050169   336.540  < 2e-16 ***
ORIGIN_SZCKSZ05  1.3932005  0.0062346   223.464  < 2e-16 ***
ORIGIN_SZCKSZ06  1.0670053  0.0066112   161.394  < 2e-16 ***
ORIGIN_SZCLSZ01 -0.8602837  0.0079240  -108.567  < 2e-16 ***
ORIGIN_SZCLSZ02 -1.3853421  0.0137444  -100.793  < 2e-16 ***
ORIGIN_SZCLSZ03 -0.8582608  0.0081177  -105.727  < 2e-16 ***
ORIGIN_SZCLSZ04  0.7836027  0.0046427   168.782  < 2e-16 ***
ORIGIN_SZCLSZ05 -1.8121756  0.0148960  -121.655  < 2e-16 ***
ORIGIN_SZCLSZ06  0.8296870  0.0043909   188.955  < 2e-16 ***
ORIGIN_SZCLSZ07 -0.2325219  0.0057432   -40.487  < 2e-16 ***
ORIGIN_SZCLSZ08  0.2714336  0.0062625    43.342  < 2e-16 ***
ORIGIN_SZCLSZ09 -2.2223744  0.0160946  -138.082  < 2e-16 ***
ORIGIN_SZDTSZ02 -4.0704970  0.0834192   -48.796  < 2e-16 ***
ORIGIN_SZDTSZ03 -3.4529031  0.0738295   -46.769  < 2e-16 ***
ORIGIN_SZDTSZ13 -2.8301983  0.0313085   -90.397  < 2e-16 ***
ORIGIN_SZGLSZ01 -1.4674986  0.0093137  -157.563  < 2e-16 ***
ORIGIN_SZGLSZ02  0.2749369  0.0050051    54.931  < 2e-16 ***
ORIGIN_SZGLSZ03  0.0781954  0.0049748    15.718  < 2e-16 ***
ORIGIN_SZGLSZ04  0.8167797  0.0043260   188.808  < 2e-16 ***
ORIGIN_SZGLSZ05  0.5277509  0.0044879   117.595  < 2e-16 ***
ORIGIN_SZHGSZ01  0.2323885  0.0048555    47.861  < 2e-16 ***
ORIGIN_SZHGSZ02  0.5707182  0.0048256   118.268  < 2e-16 ***
ORIGIN_SZHGSZ03  0.4231170  0.0052149    81.136  < 2e-16 ***
ORIGIN_SZHGSZ04  0.9341168  0.0044128   211.681  < 2e-16 ***
ORIGIN_SZHGSZ05  1.2192790  0.0043790   278.437  < 2e-16 ***
ORIGIN_SZHGSZ06  0.0490041  0.0054961     8.916  < 2e-16 ***
ORIGIN_SZHGSZ07  0.6337041  0.0045735   138.559  < 2e-16 ***
ORIGIN_SZHGSZ08  0.0312612  0.0054684     5.717 1.09e-08 ***
ORIGIN_SZHGSZ09 -0.6985397  0.0071800   -97.289  < 2e-16 ***
ORIGIN_SZHGSZ10 -2.9958967  0.0422303   -70.942  < 2e-16 ***
ORIGIN_SZJESZ01  0.4363431  0.0051329    85.010  < 2e-16 ***
ORIGIN_SZJESZ02  0.3460900  0.0051372    67.370  < 2e-16 ***
ORIGIN_SZJESZ03  0.2928005  0.0055108    53.132  < 2e-16 ***
ORIGIN_SZJESZ04 -1.1924298  0.0093540  -127.478  < 2e-16 ***
ORIGIN_SZJESZ05 -2.0178136  0.0139479  -144.668  < 2e-16 ***
ORIGIN_SZJESZ06  0.1637633  0.0050685    32.310  < 2e-16 ***
ORIGIN_SZJESZ07 -1.8227460  0.0119383  -152.680  < 2e-16 ***
ORIGIN_SZJESZ08 -1.1556281  0.0117870   -98.043  < 2e-16 ***
ORIGIN_SZJESZ09  0.4766229  0.0052813    90.248  < 2e-16 ***
ORIGIN_SZJESZ10 -2.6868992  0.0186864  -143.789  < 2e-16 ***
ORIGIN_SZJESZ11 -3.0618150  0.0199755  -153.278  < 2e-16 ***
ORIGIN_SZJWSZ01  0.4417418  0.0068611    64.383  < 2e-16 ***
ORIGIN_SZJWSZ02  0.9738087  0.0047905   203.281  < 2e-16 ***
ORIGIN_SZJWSZ03  1.1548028  0.0045180   255.599  < 2e-16 ***
ORIGIN_SZJWSZ04  0.9078417  0.0046668   194.532  < 2e-16 ***
ORIGIN_SZJWSZ05 -1.7092500  0.0127422  -134.141  < 2e-16 ***
ORIGIN_SZJWSZ06 -1.3284287  0.0109785  -121.002  < 2e-16 ***
ORIGIN_SZJWSZ07 -2.3231549  0.0281427   -82.549  < 2e-16 ***
ORIGIN_SZJWSZ08  1.9386127  0.0046041   421.059  < 2e-16 ***
ORIGIN_SZJWSZ09  1.3987549  0.0042610   328.266  < 2e-16 ***
ORIGIN_SZKLSZ01  0.2617735  0.0050089    52.261  < 2e-16 ***
ORIGIN_SZKLSZ02 -0.4325093  0.0064279   -67.286  < 2e-16 ***
ORIGIN_SZKLSZ03 -0.2787173  0.0060380   -46.161  < 2e-16 ***
ORIGIN_SZKLSZ04 -1.9432693  0.0119163  -163.076  < 2e-16 ***
ORIGIN_SZKLSZ05 -0.5420067  0.0085529   -63.371  < 2e-16 ***
ORIGIN_SZKLSZ06 -4.2949009  0.1857686   -23.120  < 2e-16 ***
ORIGIN_SZKLSZ07 -0.8576946  0.0085178  -100.694  < 2e-16 ***
ORIGIN_SZKLSZ08 -1.3840925  0.0092323  -149.918  < 2e-16 ***
ORIGIN_SZLKSZ01 -2.8108510  0.0392356   -71.640  < 2e-16 ***
ORIGIN_SZMDSZ01 -1.6745388  0.0296543   -56.469  < 2e-16 ***
ORIGIN_SZMDSZ02 -0.8193738  0.0106631   -76.842  < 2e-16 ***
ORIGIN_SZMDSZ03 -1.5088267  0.0172032   -87.706  < 2e-16 ***
ORIGIN_SZMPSZ01 -0.9860154  0.0085053  -115.929  < 2e-16 ***
ORIGIN_SZMPSZ02 -0.5958875  0.0070097   -85.008  < 2e-16 ***
ORIGIN_SZMPSZ03 -0.0490122  0.0054582    -8.980  < 2e-16 ***
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ORIGIN_SZNTSZ01 -2.6451541  0.0353125   -74.907  < 2e-16 ***
ORIGIN_SZNTSZ02 -2.7710546  0.0232841  -119.011  < 2e-16 ***
ORIGIN_SZNTSZ03 -0.6123404  0.0079083   -77.430  < 2e-16 ***
ORIGIN_SZNTSZ05 -2.9257445  0.0496704   -58.903  < 2e-16 ***
ORIGIN_SZNTSZ06 -3.3260031  0.0557966   -59.609  < 2e-16 ***
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ORIGIN_SZNVSZ03 -1.0765622  0.0078766  -136.679  < 2e-16 ***
ORIGIN_SZNVSZ04 -1.2289504  0.0091468  -134.358  < 2e-16 ***
ORIGIN_SZNVSZ05 -2.3551389  0.0158219  -148.853  < 2e-16 ***
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ORIGIN_SZPGSZ03  0.8976913  0.0046122   194.636  < 2e-16 ***
ORIGIN_SZPGSZ04  1.1161685  0.0045850   243.437  < 2e-16 ***
ORIGIN_SZPGSZ05  0.4794249  0.0060213    79.621  < 2e-16 ***
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ORIGIN_SZPLSZ03 -3.2744991  0.0374541   -87.427  < 2e-16 ***
ORIGIN_SZPLSZ04 -3.5423615  0.0372570   -95.079  < 2e-16 ***
ORIGIN_SZPLSZ05 -2.4343705  0.0227807  -106.861  < 2e-16 ***
ORIGIN_SZPNSZ01  0.8052461  0.0056124   143.476  < 2e-16 ***
ORIGIN_SZPNSZ02 -1.8042362  0.0128222  -140.712  < 2e-16 ***
ORIGIN_SZPNSZ03 -2.6363996  0.0200058  -131.782  < 2e-16 ***
ORIGIN_SZPNSZ04 -4.8427070  0.0320126  -151.275  < 2e-16 ***
ORIGIN_SZPNSZ05 -3.6613775  0.0285686  -128.161  < 2e-16 ***
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ORIGIN_SZPRSZ02  0.9145886  0.0048137   189.998  < 2e-16 ***
ORIGIN_SZPRSZ03  0.4478971  0.0048102    93.113  < 2e-16 ***
ORIGIN_SZPRSZ04 -0.5312444  0.0079019   -67.230  < 2e-16 ***
ORIGIN_SZPRSZ05  1.1462662  0.0045250   253.318  < 2e-16 ***
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ORIGIN_SZPRSZ07 -2.1667862  0.0162528  -133.318  < 2e-16 ***
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ORIGIN_SZQTSZ06 -0.2521417  0.0066449   -37.945  < 2e-16 ***
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ORIGIN_SZQTSZ12 -1.3866518  0.0106887  -129.730  < 2e-16 ***
ORIGIN_SZQTSZ13 -0.3764286  0.0066707   -56.430  < 2e-16 ***
ORIGIN_SZQTSZ14 -1.4907399  0.0100120  -148.896  < 2e-16 ***
ORIGIN_SZQTSZ15 -1.0552239  0.0108792   -96.994  < 2e-16 ***
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ORIGIN_SZRCSZ06 -0.2418276  0.0085509   -28.281  < 2e-16 ***
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ORIGIN_SZRVSZ02 -2.2980940  0.0278202   -82.605  < 2e-16 ***
ORIGIN_SZRVSZ03 -2.4663765  0.0238674  -103.336  < 2e-16 ***
ORIGIN_SZRVSZ04 -3.1853677  0.0556939   -57.194  < 2e-16 ***
ORIGIN_SZRVSZ05 -1.5695490  0.0166684   -94.163  < 2e-16 ***
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ORIGIN_SZSBSZ02 -0.7307279  0.0084105   -86.883  < 2e-16 ***
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ORIGIN_SZSBSZ04  0.3684857  0.0058575    62.908  < 2e-16 ***
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ORIGIN_SZSBSZ06 -1.1939284  0.0181541   -65.766  < 2e-16 ***
ORIGIN_SZSBSZ07 -0.4896579  0.0135618   -36.106  < 2e-16 ***
ORIGIN_SZSBSZ08 -2.1221691  0.0127258  -166.762  < 2e-16 ***
ORIGIN_SZSBSZ09 -1.2032410  0.0089611  -134.273  < 2e-16 ***
ORIGIN_SZSESZ02  1.0721820  0.0045336   236.498  < 2e-16 ***
ORIGIN_SZSESZ03  1.0808012  0.0042923   251.801  < 2e-16 ***
ORIGIN_SZSESZ04  1.0137448  0.0050668   200.076  < 2e-16 ***
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ORIGIN_SZSESZ07 -2.2499789  0.0196327  -114.603  < 2e-16 ***
ORIGIN_SZSGSZ01 -0.9369800  0.0087282  -107.351  < 2e-16 ***
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ORIGIN_SZSGSZ03  0.2604352  0.0052709    49.410  < 2e-16 ***
ORIGIN_SZSGSZ04  0.3468823  0.0048897    70.942  < 2e-16 ***
ORIGIN_SZSGSZ05 -1.5927797  0.0106308  -149.827  < 2e-16 ***
ORIGIN_SZSGSZ06  0.3605651  0.0046361    77.774  < 2e-16 ***
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ORIGIN_SZSKSZ02  0.0970953  0.0063378    15.320  < 2e-16 ***
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ORIGIN_SZSKSZ05 -1.5443140  0.0179059   -86.246  < 2e-16 ***
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ORIGIN_SZSRSZ01 -1.6136735  0.0160199  -100.729  < 2e-16 ***
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ORIGIN_SZTMSZ02  1.6667504  0.0039836   418.403  < 2e-16 ***
ORIGIN_SZTMSZ03  1.0941176  0.0042911   254.976  < 2e-16 ***
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ORIGIN_SZTMSZ05 -0.8155124  0.0079342  -102.785  < 2e-16 ***
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ORIGIN_SZTNSZ03 -1.7960517  0.0134675  -133.362  < 2e-16 ***
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ORIGIN_SZTPSZ01 -0.3841699  0.0064137   -59.898  < 2e-16 ***
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ORIGIN_SZTPSZ08 -0.6976429  0.0092416   -75.490  < 2e-16 ***
ORIGIN_SZTPSZ09 -0.3708833  0.0063548   -58.363  < 2e-16 ***
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ORIGIN_SZTSSZ04 -0.6380676  0.0099905   -63.867  < 2e-16 ***
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ORIGIN_SZTSSZ06 -2.6310865  0.0255772  -102.868  < 2e-16 ***
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ORIGIN_SZWDSZ02  0.9119539  0.0050326   181.210  < 2e-16 ***
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DESTIN_SZRVSZ05 -2.3683855  0.0259334   -91.326  < 2e-16 ***
DESTIN_SZSBSZ01 -0.5841063  0.0068588   -85.162  < 2e-16 ***
DESTIN_SZSBSZ02 -1.0777704  0.0078288  -137.667  < 2e-16 ***
DESTIN_SZSBSZ03  0.4734371  0.0045880   103.190  < 2e-16 ***
DESTIN_SZSBSZ04  0.0546094  0.0057517     9.494  < 2e-16 ***
DESTIN_SZSBSZ05 -0.9588198  0.0075242  -127.431  < 2e-16 ***
DESTIN_SZSBSZ06 -1.8528944  0.0234040   -79.170  < 2e-16 ***
DESTIN_SZSBSZ07 -1.8403768  0.0195878   -93.955  < 2e-16 ***
DESTIN_SZSBSZ08  0.9205969  0.0055698   165.285  < 2e-16 ***
DESTIN_SZSBSZ09  0.5166486  0.0051939    99.472  < 2e-16 ***
DESTIN_SZSESZ02 -0.5728211  0.0048270  -118.669  < 2e-16 ***
DESTIN_SZSESZ03  0.2554787  0.0038335    66.645  < 2e-16 ***
DESTIN_SZSESZ04 -0.8982794  0.0056698  -158.432  < 2e-16 ***
DESTIN_SZSESZ05 -0.4661655  0.0048578   -95.962  < 2e-16 ***
DESTIN_SZSESZ06 -0.8392849  0.0059198  -141.777  < 2e-16 ***
DESTIN_SZSESZ07 -3.2182325  0.0227089  -141.717  < 2e-16 ***
DESTIN_SZSGSZ01 -0.2751206  0.0059581   -46.176  < 2e-16 ***
DESTIN_SZSGSZ02 -0.2951806  0.0052515   -56.209  < 2e-16 ***
DESTIN_SZSGSZ03 -0.4469508  0.0048181   -92.766  < 2e-16 ***
DESTIN_SZSGSZ04 -0.2842809  0.0047961   -59.274  < 2e-16 ***
DESTIN_SZSGSZ05 -2.0643753  0.0098252  -210.109  < 2e-16 ***
DESTIN_SZSGSZ06  0.2501247  0.0038873    64.343  < 2e-16 ***
DESTIN_SZSGSZ07 -0.5743750  0.0052184  -110.067  < 2e-16 ***
DESTIN_SZSISZ01 -1.1030669  0.0259113   -42.571  < 2e-16 ***
DESTIN_SZSKSZ01 -0.5462538  0.0071443   -76.460  < 2e-16 ***
DESTIN_SZSKSZ02  0.2965180  0.0056707    52.290  < 2e-16 ***
DESTIN_SZSKSZ03 -0.4521490  0.0062177   -72.719  < 2e-16 ***
DESTIN_SZSKSZ04 -0.6665145  0.0148252   -44.958  < 2e-16 ***
DESTIN_SZSKSZ05 -0.1474142  0.0121958   -12.087  < 2e-16 ***
DESTIN_SZSLSZ01 -0.8855715  0.0084587  -104.693  < 2e-16 ***
DESTIN_SZSLSZ04 -1.1787840  0.0071355  -165.200  < 2e-16 ***
DESTIN_SZSRSZ01 -1.6435064  0.0128822  -127.580  < 2e-16 ***
DESTIN_SZTHSZ01 -3.4388625  0.0367651   -93.536  < 2e-16 ***
DESTIN_SZTHSZ03 -2.5809435  0.0256853  -100.483  < 2e-16 ***
DESTIN_SZTHSZ04 -2.4887189  0.0214441  -116.056  < 2e-16 ***
DESTIN_SZTHSZ06 -1.7965101  0.0152160  -118.067  < 2e-16 ***
DESTIN_SZTMSZ01 -0.3251891  0.0058067   -56.002  < 2e-16 ***
DESTIN_SZTMSZ02  1.1558743  0.0034703   333.080  < 2e-16 ***
DESTIN_SZTMSZ03  0.4525619  0.0039244   115.319  < 2e-16 ***
DESTIN_SZTMSZ04  0.8223271  0.0040060   205.274  < 2e-16 ***
DESTIN_SZTMSZ05  0.3880619  0.0054308    71.456  < 2e-16 ***
DESTIN_SZTNSZ01 -0.9533112  0.0067853  -140.496  < 2e-16 ***
DESTIN_SZTNSZ02 -1.5909451  0.0097396  -163.348  < 2e-16 ***
DESTIN_SZTNSZ03 -1.6470771  0.0116598  -141.261  < 2e-16 ***
DESTIN_SZTNSZ04 -1.0686173  0.0069848  -152.993  < 2e-16 ***
DESTIN_SZTPSZ01 -0.5180183  0.0056886   -91.063  < 2e-16 ***
DESTIN_SZTPSZ02  0.2160781  0.0038283    56.443  < 2e-16 ***
DESTIN_SZTPSZ03 -0.2479956  0.0056651   -43.776  < 2e-16 ***
DESTIN_SZTPSZ04 -1.5015463  0.0072444  -207.271  < 2e-16 ***
DESTIN_SZTPSZ05 -0.9551144  0.0057981  -164.729  < 2e-16 ***
DESTIN_SZTPSZ06 -0.4846634  0.0074621   -64.950  < 2e-16 ***
DESTIN_SZTPSZ07 -1.9753440  0.0118295  -166.984  < 2e-16 ***
DESTIN_SZTPSZ08 -1.3455063  0.0086909  -154.817  < 2e-16 ***
DESTIN_SZTPSZ09 -0.3556620  0.0061296   -58.024  < 2e-16 ***
DESTIN_SZTPSZ10 -1.3213501  0.0085951  -153.733  < 2e-16 ***
DESTIN_SZTPSZ11 -0.3877006  0.0052409   -73.977  < 2e-16 ***
DESTIN_SZTPSZ12 -0.7064020  0.0062472  -113.075  < 2e-16 ***
DESTIN_SZTSSZ01 -0.8827157  0.0218327   -40.431  < 2e-16 ***
DESTIN_SZTSSZ02 -0.6067055  0.0115514   -52.522  < 2e-16 ***
DESTIN_SZTSSZ03  0.4380259  0.0086774    50.479  < 2e-16 ***
DESTIN_SZTSSZ04  0.4902124  0.0089922    54.515  < 2e-16 ***
DESTIN_SZTSSZ05  1.4336278  0.0093410   153.477  < 2e-16 ***
DESTIN_SZTSSZ06  0.9223573  0.0209024    44.127  < 2e-16 ***
DESTIN_SZWCSZ01  1.1559309  0.0051787   223.208  < 2e-16 ***
DESTIN_SZWCSZ02 -1.2664455  0.0126131  -100.407  < 2e-16 ***
DESTIN_SZWCSZ03 -2.7360882  0.0325753   -83.993  < 2e-16 ***
DESTIN_SZWDSZ01  0.8193492  0.0037301   219.657  < 2e-16 ***
DESTIN_SZWDSZ02 -0.7852474  0.0058655  -133.875  < 2e-16 ***
DESTIN_SZWDSZ03  0.5742422  0.0041884   137.104  < 2e-16 ***
DESTIN_SZWDSZ04 -0.8391525  0.0065075  -128.951  < 2e-16 ***
DESTIN_SZWDSZ05 -0.3510692  0.0057253   -61.319  < 2e-16 ***
DESTIN_SZWDSZ06  0.1358804  0.0043968    30.905  < 2e-16 ***
DESTIN_SZWDSZ07 -0.2207379  0.0066369   -33.259  < 2e-16 ***
DESTIN_SZWDSZ08 -0.0264655  0.0065065    -4.068 4.75e-05 ***
DESTIN_SZWDSZ09 -0.2065828  0.0050524   -40.888  < 2e-16 ***
DESTIN_SZYSSZ01  0.7467996  0.0040979   182.238  < 2e-16 ***
DESTIN_SZYSSZ02 -0.3002718  0.0053434   -56.195  < 2e-16 ***
DESTIN_SZYSSZ03 -1.1087686  0.0057219  -193.778  < 2e-16 ***
DESTIN_SZYSSZ04 -0.3748076  0.0051481   -72.805  < 2e-16 ***
DESTIN_SZYSSZ05 -1.7909654  0.0102064  -175.475  < 2e-16 ***
DESTIN_SZYSSZ06 -1.8519179  0.0099601  -185.933  < 2e-16 ***
DESTIN_SZYSSZ07 -0.9246626  0.0118101   -78.294  < 2e-16 ***
DESTIN_SZYSSZ08  0.4403129  0.0041268   106.697  < 2e-16 ***
DESTIN_SZYSSZ09  0.0267012  0.0041393     6.451 1.11e-10 ***
log(dist)       -0.6721961  0.0001353 -4969.566  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 60796037  on 14733  degrees of freedom
Residual deviance: 20988409  on 14175  degrees of freedom
AIC: 21081154

Number of Fisher Scoring iterations: 7

We can examine how the constraints hold for destinations this time.

Code

CalcRSquared(dbcSIM$data$TRIPS, dbcSIM$fitted.values)

[1] 0.5739638

Notice that there is a relatively greater improvement in the R^2 value.

6.9 Model comparison

Another useful model performance measure for continuous dependent variable is Root Mean Squared Error. In this sub-section, you will learn how to use compare_performance() of performance package

First of all, let us create a list called model_list by using the code chun below.

Code

model_list <- list(unconstrained=uncSIM,
                   originConstrained=orcSIM,
                   destinationConstrained=decSIM,
                   doublyConstrained=dbcSIM)

Next, we will compute the RMSE of all the models in model_list file by using the code chunk below.

Code

compare_performance(model_list,
                    metrics = "RMSE")

# Comparison of Model Performance Indices

Name                   | Model |     RMSE
-----------------------------------------
unconstrained          |   glm | 4288.012
originConstrained      |   glm | 3659.954
destinationConstrained |   glm | 3389.556
doublyConstrained      |   glm | 3252.297

The print above reveals that doubly constrained SIM is the best model among all the four SIMs because it has the smallest RMSE value of 1487.111.

6.10 Visualising fitted values

In this section, you will learn how to visualise the observed values and the fitted values.

Firstly we will extract the fitted values from each model by using the code chunk below.

Code

df <- as.data.frame(uncSIM$fitted.values) %>%
  round(digits = 0)

Next, we will join the values to SIM_data data frame.

Code

SIM_data <- SIM_data %>%
  cbind(df) %>%
  rename(uncTRIPS = "uncSIM$fitted.values")

Repeat the same step by for Origin Constrained SIM (i.e. orcSIM)

Code

df <- as.data.frame(orcSIM$fitted.values) %>%
  round(digits = 0)

Code

SIM_data <- SIM_data %>%
  cbind(df) %>%
  rename(orcTRIPS = "orcSIM$fitted.values")

Repeat the same step by for Destination Constrained SIM (i.e. decSIM)

Code

df <- as.data.frame(decSIM$fitted.values) %>%
  round(digits = 0)

Code

SIM_data <- SIM_data %>%
  cbind(df) %>%
  rename(decTRIPS = "decSIM$fitted.values")

Repeat the same step by for Doubly Constrained SIM (i.e. dbcSIM)

Code

df <- as.data.frame(dbcSIM$fitted.values) %>%
  round(digits = 0)

Code

SIM_data <- SIM_data %>%
  cbind(df) %>%
  rename(dbcTRIPS = "dbcSIM$fitted.values")

Code

unc_p <- ggplot(data = SIM_data,
                aes(x = uncTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

orc_p <- ggplot(data = SIM_data,
                aes(x = orcTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

dec_p <- ggplot(data = SIM_data,
                aes(x = decTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

dbc_p <- ggplot(data = SIM_data,
                aes(x = dbcTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

Now, we will put all the graphs into a single visual for better comparison by using the code chunk below.

Code

ggarrange(unc_p, orc_p, dec_p, dbc_p,
          ncol = 2,
          nrow = 2)